Despite taking an impressive 20 points from their opening 10 games in the Premier League this season, Spurs have hit the net just nine times.
Only Stoke City, Sunderland and Crystal Palace have scored fewer top-flight goals this term and, as a result, Villas-Boas is believed to be keen on bolstering his attacking options.
According to The Telegraph, Villas-Boas will make a bid for Hernandez when the transfer window reopens, but only if he is able to offload out-of-favour striker Emmanuel Adebayor.
Hernandez, 25, has netted 34 goals in 81 Premier League games for United since making his debut in August 2010. Only 43 of the Mexico international's top-flight appearances have been starts.