The 25-year-old midfielder has scored 11 times for the U's in 82 appearances since joining from Luton in the summer of 2010.
However, his time at the Kassam Stadium appears to be at an end after Oxford chairman Kelvin Thomas revealed he has received an attractive offer from another club.
He told his club's official website: "We made Asa what we considered a decent offer on improved terms, but to be fair to Asa he was honest with us and has been offered a contract on quite a bit more money closer to home and in a higher division."
Thomas went on to confirm that other contractual discussions are also underway.
He added: "At the same time conversations continue with Wayne Brown and Adam Chapman, who have also been offered new deals and hopefully we can get those tied up soon."