The defender looked destined to leave Craven Cottage after rejecting a new deal in June but could now restart dialogue after boss Marco Silva extended his own stay until 2026.
Monaco had an £8.5million bid for the player snubbed in August, while Tottenham are also admirers of Tosin.
The 26-year-old, whose current deal expires next summer, can sign a pre-contract agreement with clubs overseas from January 1.
Fulham hope to have Tosin back from injury in the coming weeks after he underwent groin surgery. They are short of options at the back, with Issa Diop also currently out injured.
Left-footed option Calvin Bassey, meanwhile, put in an uncomfortable performance on the right side of defence and made crucial mistakes in the build-up to both of Tottenham's goals in the 2-0 Premier League defeat on Monday night.
Bassey, a £19.3m summer arrival from Ajax, was also sent off on his full top-flight debut against Arsenal earlier this season.