Villas-Boas admitted he attempted to sign the striker prior to his move to Stamford Bridge last summer but were thwarted by a change in league regulations by the Russian Football Union (RFU) in July.
Rules stipulate teams must field no more than six foreign players at any one time – one fewer than the previous year – and, as Zenit currently have eight foreign first-team players, a move is '"difficult".
"No I haven’t had a conversation with Jose, the player belongs to Chelsea, on loan from Monaco," he told the club's official website ahead of their league clash with Mordovia.
"It’s difficult to bring such a player to Russia with the rules and regulations we have.
"We tried to bring him here in the summer at the start of the season, but then the rules changed a week before the season started.
"We can’t bring him here because of the rules and we don’t have space.
Zenit signed Russia international Artyom Dzyuba during the summer with the striker scoring 11 goals since arriving from Spartak Moscow, including a brace in a 5-1 win over Anzhi Makhachkala on Saturday.
Villas-Boas feels a combination of Dzybua’s form and the fact that Russian Sports Minister Vitaly Mutko is backing a €31,000-a-month player salary cap means a move for Falcao is now out of the question.
He said: "We have Dzyuba, he scored two goals, his form is great for the club and the national team and he deserves respect.
"Due to the limitations we can’t bring Falcao here, his salary is immense too and the financial rules in place prevent this, this is the rule chosen by Mr Mutko and the so this is impossible."