The report claims that Spurs made a direct offer but that Fenerbahçe president Aziz Yıldırım turned down the bid.
Topal has a year left on his contract but has yet to extend his current deal with the Yellow Canaries.
The 29-year-old midfielder has won the league title twice. Once with Galatasaray and the other with bitter rivals Fenerbahçe.
Topal also has experience playing abroad, the experienced midfielder had a spell in Spain with Valencia following his stint at Galatasaray.
The experienced midfielder’s agent Batur Altıparmak recently stated that he expects his client to stay in Istanbul for the 2015-16 season.
“Mehmet is likely to be at Fenerbahçe next season,” Altıparmak told Turkish-football.com.
The dual-footed defensive midfielder nicknamed ‘spiderman’ has provided four assists and four goals in 41 appearances for Fenerbahçe in all competitions last season.
Fenerbahçe will compete in the Europa League this season and are managed by Vitor Pereira.