Smalling, 25, joined United from Fulham back in 2010 - despite playing just 19 games for the Cottagers after a move from non-league side Maidstone United.
Dubbed as one of the brightest English prospects at the time, Smalling has struggled to live up to the hype in recent years, but is playing his best football under van Gaal this season.
His recent performances have been outstanding, particularly against Liverpool on Sunday, where he largely kept Daniel Sturridge quiet.
However, with his contract set to expire in just over a year, reports from the Daily Mirror earlier this week suggested that Arsenal were interested in signing Smalling in a £12m deal this summer.
That would be Arsenal's third attempt at signing Smalling, having failed in 2010 and 2014, but the Manchester Evening News believe any bids from Arsene Wenger's men would fall on deaf ears.
They report that van Gaal would reject any offers for Smalling, because the Dutchman is impressed with his recent displays and believes he's finally hitting his potential.
That would leave Arsenal looking for another centre back, despite the January signing of Gabriel Paulista from Villarreal, who has already dislodged Per Mertesacker in the starting line-up.