Spurs boss Mauricio Pochettino left Janssen out of his squad for the International Champions Cup tour of the United States this summer after ruling that the striker is surplus to requirements ahead of the 2018-19 campaign.
The North London club signed Janssen from AZ Alkmaar for £17.5m two years ago after he finished the previous season as the Eredivisie's top scorer with 27 goals in 34 appearances.
However, he failed to establish himself in Pochettino's team, netting just six times in all competitions the following campaign.
"It's different personal situations for different players," Pochettino told reporters.
"It's clear the situation for players like Vincent. But Josh is part of our plans. He's injured and doing his recovery with Harry Winks. That's why he's not here."
Fenerbahce are said to be looking to re-sign Janssen from Tottenham Hotspur on a loan deal, with a mandatory redemption clause, according to Turkish newspaper Sabah.
The Dutchman, 24, was sent on loan to the Turkish side last term, scoring four goals in 16 games.