The 23-year old midfielder has fallen down the pecking order at White Hart Lane this season and could go out to play regular first-team football according to Villas-Boas.
"There is a couple of possibilities for Jake to get a loan deal," Villas-Boas said.
"We are pretty happy with how he trains and how professional he has been but he hasn't had a lot of [playing] time.
"He is aware of these conversations. We just have to wait and see."
Livermore made 38 appearances under Harry Redknapp last season and there has been some interest in the former Spurs boss and the midfielder reuniting at QPR.