Tottenham signed the winger on loan from Juventus in January last year with a view to signing him on a permanent deal.
Juventus inserted an obligation to buy for €35m provided Spurs qualified for the Champions League this season.
With Spurs not qualifying for Europe’s elite club competition, the north London club are no longer expected to sign him on a permanent deal.
And according to Italian daily Il Messaggero, the winger is now attracting interest from Serie A giants Lazio.
The Roman club have qualified for the Champions League this season and are looking to invest in their squad.
Maurizio Sarri wants a winger for his team and the Spurs attacker has emerged as a top target for the club.
Juventus control the Swede’s future at the moment and they could be willing to let him move to Lazio this summer.
They are considering using Lazio’s interest in Kulusevski in order to sign Sergej Milinkovic-Savic in a swap deal.