Wolves' Bakary Sako has revealed he is mulling over offers from the Premier League but is yet to decide on his future.
Rotherham boss Steve Evans will decide the fate of his out-of-contract players in a meeting on Monday.
The 27-year-old is reunited with Royals boss Nigel Adkins, who managed him at St Mary's and also at Scunthorpe.
Sharp has scored 140 career goals but has not made an appearance for Southampton since August 2012, his last action coming in a loan spell with Nottingham Forest last season.
Nevertheless he will go straight into the Reading squad for Saturday's visit of Birmingham.