Spanish newspaper AS claims Spurs would be willing to pay between €20m and €30m for the Montenegrin forward, who could be available if Gonzalo Higuain joins the Serie 'A' champions from the Bernabeu.
The transfer domino effect could see Bale joining Real Madrid, allowing Higuain to move to Juventus, which would see Tottenham using the transfer windfall from the Bale sale to finance a move for Vucinic.
The report claims Real Madrid president Florentino Perez has set aside €70m for Gareth Bale. The Spanish giants want to conclude a deal quickly before Bale agrees a new contract with Tottenham.
Spurs have been linked with several strikers in recent weeks. After missing out on Champions League qualification, Andre Villas-Boas wants to strengthen his squad heavily, with the main priority a frontman.
Jermain Defoe's injury niggles and Emmanuel Adebayor's poor form in front of goal can be partly blamed for Tottenham's failure to clinch a top four spot, and the north London club have been linked with Leandro Damiao, David Villa and Roberto Soldado.
But Vucinic could be available this summer as Juventus have already agreed a deal to bring Athletic Bilbao and Spain international Fernando Llorente to the club this summer.
And if Higuain completes his move from the Bernabeu, the 29-year-old Vucinic may be deemed surplus to requirements.
Last season Vucinic joint-top scored for the Italian champions in the league, bagging 10 goals in 24 starts.