James Constable is set for talks with Swindon Town manager Paolo Di Canio tonight over a potential move to the County Ground.
Two offers for the 27-year-old striker were rejected by the U's last week.
But the Robins have come back with what United call a 'much-improved' bid, and the U's have today accepted it.
The decision on whether the transfer goes ahead now lies at the feet of Constable.
The fee is believed to be between £250,000 and £300,000.
A statement from the U's reads: "Oxford United Football Club can confirm they have received a much improved offer from Swindon Town Football Club for James Constable and after discussions with the player have given permission for him to talk to the club.
"Until this situation is resolved there will be no further comment from the club."
Swindon manager Paolo Di Canio confirmed that the club were looking to sign a new striker in his weekly press conference today, but refused to identify Constable by name, instead saying: "I hope to have someone very soon. Someone not so far from here.
"I hope we are close, but until I see a signature I don't want to say anymore."
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