The new Spurs boss began his time in charge of the Premier League club with a defeat at Newcastle on Saturday’s first day of the new season.
Modric was missing from the Tottenham side as negotiations continue between the London club’s chairman, Daniel Levy, and Spanish champions Real Madrid over a deal in the region of £30million.
Villas-Boas has made little secret of the fact he wants the money to reinvest in a new striker and that need was highlighted against Newcastle, with Jermain Defoe having to play in a lone role.
And asked after the defeat whether he is ready to sign a striker with the money from the sale of Modric, the former Chelsea manager told ESPN: “We have been very, very active looking for different solutions. For one reason or another, it has not happened so far.
“But we are confident we can close it down in the next couple of days. If that is the case he (Levy) will further strengthen the squad with what we are looking for.”
Modric, who could also be a target of Chelsea, may yet move to Real on Sunday and talks are continuing between the Primera Liga club and Levy.
Asked if the Croatia international will depart this weekend, Villas-Boas said: “Negotiations are ongoing so it could happen.”
Villas-Boas was disappointed by Tottenham’s defeat at St James’ Park, where an excellent Demba Ba strike and a Hatem Ben Arfa penalty sandwiched Defoe’s equaliser.
A poor defensive header by Kyle Walker in the build-up to the Ba goal and sloppy defending from Rafael van der Vaart and Aaron Lennon at the penalty were what cost Spurs.
And Villas-Boas said: “Maybe we could have done slightly better on closing down Demba Ba. He is obviously a top goalscorer.
“On the penalty incident, when a player goes through two players, it is a difficult call for the referee.”