generously, graciously, kindly
She graciously offered to get pizza so I wouldn't have to cook.

helpfully
freely
Hospitality was freely offered to refugees.

be able to, be unable to, can
the protection that life insurance can offer

appear to, seem to
The plan seemed to offer real advantages.

fail to
be pleased to (formal), would like to
I refer to your recent application and interview and am pleased to offer you the post of editor.

aim to, seek to
claim to
They claim to offer a more comprehensive service than other companies.

be expected to, be likely to
This investment is likely to offer a higher return.

be compelled to, be forced to, be obliged to
feel compelled to, feel obliged to
She felt obliged to offer him a bed for the night.

have little to, have a lot to, have nothing to, have something to, etc.
This player has proved that he still has a lot to offer (= can still play well).

have sth to
a chance to see what the college has to offer students

to
She offered drinks to her guests.

be able to, be unable to, can
be prepared to, be ready to, be willing to
Would they be prepared to offer any more?

for
They have offered over £500 000 for the house.

Offer is used with these nouns as the subject:
approach, clinic, college, competitor, dealer, design, district, edition, hotel, magazine, menu, programme, religion, restaurant, scheme, shop, site, store, system, website

Offer is used with these nouns as the object:
access, accommodation, account, advantage, adventure, advice, alternative, amendment, amenity, amnesty, answer, antidote, apology, appointment, arbitration, argument, array, assessment, assistance, assurance, asylum, benefit, blueprint, bribe, bursary, carrot, challenge, chance, choice, clarification, clarity, class, clue, comfort, comment, commentary, compensation, compromise, concession, condolences, congratulations, consolation, consumer, context, contract, contrast, contribution, convenience, cooperation, counsel, counselling, coupon, course, coverage, crèche, credit, criticism, critique, crown, cuisine, cup, curriculum, deal, defence, definition, description, detail, discount, drink, education, efficiency, employment, encouragement, endorsement, entertainment, escape, evidence, example, excursion, excuse, experience, expertise, explanation, facility, fare, feature, feedback, flexibility, food, forgiveness, forum, framework, freedom, gift, glimpse, grant, greeting, guarantee, guidance, guideline, haven, help, hint, hope, hospitality, idea, illustration, improvement, incentive, inducement, information, insight, instruction, insurance, interpretation, introduction, job, justification, knighthood, lesson, lifeline, lift, loan, look, luxury, mass, means, membership, menu, merchandise, mix, narrative, observation, odds, opinion, opportunity, option, overdraft, overview, package, parallel, pardon, perspective, place, pointer, political asylum, portrait, portrayal, position, possibility, potential, praise, prayer, prediction, prize, product, programme, promotion, proof, proposal, prospect, protection, range, rate, reading, reassurance, rebate, rebuke, recipe, recommendation, redemption, reduction, reflection, refreshment, refuge, refund, relief, remark, remedy, reminder, reply, representation, reprieve, resignation, resistance, resolution, respite, retreat, return, reward, ride, salvation, sanctuary, saving, scenario, scholarship, scope, seat, seating, selection, seminar, service, session, settlement, shade, shelter, solace, solution, subject, subsidy, suggestion, sum, summary, supervision, support, syllabus, sympathy, taste, testimony, thanks, tip, tour, truce, tuition, tutorial, twist, update, use, value, variety, venue, version, view, viewer, viewpoint, vision, wage, warranty, wealth, workshop

generous, kind
conditional, unconditional (both esp. BrE)
The company has made a conditional offer.
She received a conditional offer from the University of Warwick. (BrE)

job
peace (usually peace offering)

make (sb)
He made me an offer I simply couldn't refuse.

withdraw
get, have, receive
accept, take, take up
decline, refuse, turn down
consider

on offer
the range of goods on offer

offer from
I had to turn down a job offer from a publisher because the pay was too low.

offer of
They refused our offer of help.

special
cheap (BrE)
The council do cheap offers on compost bins.

free
I got the conditioner in a free offer with my shampoo.

introductory
Your first order is delivered free as an introductory offer.

on offer (BrE)
We have a number of bargains on offer.

acceptable, attractive, fair, good, reasonable
The company says it has made a good offer which cannot be improved upon.
$500 is my best offer (= the highest price I will offer).

tempting
high, low
We realized we would not get a higher offer.

first, initial
Don't just accept the first offer.

final
firm, formal
No one has made a firm offer.

lucrative
pay (BrE)
The union has voted for industrial action after rejecting a pay offer.

takeover
cash (esp. BrE), tender (both business)
a cash offer of $21 a share

contract (sports)
The Rams have made him a two-year contract offer.

make (sb), put in
withdraw
get, receive
consider, listen to
I'll listen to any reasonable offer.

accept, take
reject, turn down
increase, up
They just kept upping their offer until I had to say yes.

match
We should be able to match their offer for the player.

price

under offer (BrE)
The property is currently under offer to a client.

offer for
Several people put in an offer for the house.

offer of
They accepted our offer of £80 000.

be open to offers (esp. BrE)
The asking price is £500 but I'm open to offers.

or best offer (abbreviated to o.b.o)
Excellent condition. $1 000 or best offer.

or near offer, or nearest offer (abbreviated to o.n.o)
They are selling their car for £2 500 or near offer.