Baptistao has been one of the most impressive performers in La Liga this season and has helped to fill the void at Vallecano following Michu's departure to Swansea City.
The 20-year-old has attracted admiring glances from several clubs and reports in Spain claimed United scout Martin Ferguson watched the Brazilian in the 3-1 win over Getafe earlier this week.
The likes of Liverpool and Wigan Athletic are also reported to have had representatives at the game, but Vallecano have not fielded any bids for Baptistao.
Vallecano are aware that scouts have been watching the forward, but are hoping to hang on to Baptistao until the end of the season before making a decision on any offers.
Atletico Madrid are also rumoured to be keen on the player, with cash-strapped Vallecano set to demand at least €6million (£5m) before agreeing to Baptistao's sale.
Meanwhile, another reported Premier League target Piti has urged his team-mate to see out the rest of the season with Vallecano.
"Leo is tremendous. He gives us a lot because he loves to beat players, score goals and more," said Piti in the Spanish media.
"The truth is we cannot ask for more off him, he can only continue to impress. He is very focused and wants be even better but I just hope that he stays with us all season."