Kenya international Wanyama has had a transfer request rejected amid interest from Tottenham Hotspur, while the Saints have reportedly rebuffed an approach for forward Sadio Mane from Manchester United.
"The main thing is not letting anyone go," the report quoted Fonte as saying.
"That would be a help to us once the transfer window is closed and hopefully no one will leave, and possibly add a couple more, so we will see."
Southampton have already sold midfielder Morgan Schneiderlin to Manchester United and full-back Nathaniel Clyne to Liverpool this summer.
They have released another four players and have seen goalkeeper Artur Boruc join Bournemouth on a free transfer and 19-year-old forward Sam Gallagher join Championship side MK Dons on loan.
Fonte revealed that he and his teammates had spoken to the 24-year-old Wanyama, who was dropped for Sunday's 3-0 Premier League win over Norwich City.
"We all had conversations with him and try to explain (why he should stay), so now it's up to the club and to him," the 31-year-old Fonte said.
The win against Norwich, Southampton's first of the season, moved them up to 10th in the table on five points. The Saints travel to West Bromwich Albion on Sept. 12, when the league resumes after the international break.
(Reporting by Simon Jennings in Bengaluru; editing by Sudipto Ganguly)
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