Southampton have offered Jay Rodriguez a new long-term contract, sources told ESPN FC.
The England international's current deal expires in 2016 and Saints have moved to keep the former Burnley player.
Rodriguez has been monitored by Liverpool, Manchester City and Tottenham and his value in the transfer market will reduce as he enters the final year of his current deal.
The forward is yet to decide whether to accept the offer on the table and will have further discussions with the club but has been encouraged by their progress this season under manager Ronald Koeman.
The 25-year-old is yet to play this season after suffering a crucial element ligament injury 13 months ago and then having a setback, but he is back in first-team training and is closing in on a return.
Rodriguez scored 15 league goals last season while operating on the left wing, which made him of interest to some of the division's biggest clubs.
Southampton had begun contract talks with him before he was injured and have now made an improved offer.
Southampton have also offered a new deal to right-back Nathaniel Clyne, who is also out of contract in 2016.