Oxford have now turned down two bids for the 27-year-old, scorer of 11 goals last season.
Rotherham United meanwhile have continued their big summer rebuilding job with the signing of Icelandic international Kari Arnason on a free transfer from Aberdeen.
Millers manager Steve Evans, who has now made seven signings since the end of the season, told his club website: "Kari is without doubt an oustanding talent.
"The lad is technically outstanding, he is very creative in the attacking third and his all-round range of passing is top class."
Former Cobblers midfielder Danny Jackman has signed a new one-year deal with Gillingham where he was the Kent club's player of the year in 2011/12.