The 32-year-old goalkeeper is out of contract this summer and Wotte will not know if he can offer his player of the year a new deal until the club's financial situation has been resolved.
But after meeting with the former Sunderland man on Tuesday, Wotte is confident his future could still lie at St Mary's despite interest from a number of other clubs, including Leeds.
"I had a good meeting with Kelvin Davis and it was a very positive conversation," Wotte told his club's official website.
"He has always said that he is keen to stay at Southampton if we can all agree an appropriate offer,
"It is in Kelvin's hands now. We have outlined a provisional offer to him, but of course, it is dependant on us getting the go-ahead once the financial situation is more clear."
Wotte has also told young keeper Michael Poke he has a future at Saints after his successful loan spell at Torquay.