Sharp is surplus to requirements at St Mary's this summer, after Saints boss Mauricio Pochettino decided that the forward was not part of his plans.
He told Sky Sports News: "Celtic are a massive club that attracts huge crowds.
"It is a massive club with European football, so why not. Whatever happens I will decide when I cross that road, if it is Southampton or somebody else."
The 27-year-old spent last season on loan at Championship side Nottingham Forest, scoring 11 times in 31 appearances.