The Italian club previously demanded £17.5m for the 27-year-old, but have lowered their asking price following the arrival of Bojan Krkic from Barcelona, according to Goal.com.
Despite the player's agent claiming he is in talks to move to Old Trafford, Spurs are reportedly hoping to complete the signing of the Montenegrin in the next couple of days, prior to chairman Daniel Levy's holiday.
"I met Manchester United," his agent told La Signora in Giallorosso. "We spoke about Vucinic, but we didn't reach an agreement. United like Vucinic but there's still a lot of work to do to see Mirko at Old Trafford."
The striker joined the Giallorossi from fellow Italian side Lecce in 2006 for a total of €7m.