I see you have at least 3 listings that are auction format with Best Offer option. Of course offers sent that way are permitted, that's what the option is there for.
If you mean instead that you got a "Message from a member" containing an offer, you can (if there are least 12 hours left to run) but it is usually not in the seller's best interest to accept such unsolicited offers, especially if there has ever been a bid (the Best Offer option ends once there has ever been a bid). They are frequently made by scammers but even at best are made because the offeror a) doubts that the amount would win if the auction goes to the end and/or b) is 1) chronically and/or 2) situationally impatient. To accept it you have to cancel all bids and end the listing early without a winner (ticking off your existing and prospective bidders and incurring an extra fee) and then relist the item in a manner that allows the offeror to buy it properly at the correct price, with no guarantee that s/he will do so (it is likely s/he has made multiple such offers). If there has not been a bid (and at least 12 hours) you can revise the listing to add a Buy It Now--of at least 30% more than the Starting Price--or Best Offer (or both).
