Van Gaal needs to keep pace with the top four if he is to hold on to his post at Old Trafford after coming under pressure for much of the season.
United currently sit in sixth place in the Premier League, and are two points behind fourth-placed Tottenham Hotspur.
The report says that the hierarchy at the club are becoming increasingly concerned at the prospect of being cut adrift from the top four, therefore missing out on qualification for next season's Champions League.
It also states that they are prepared to give the Dutchman sufficient backing in the transfer market to make the improvements he thinks are required.
United are about to enter a crucial spell in their Premier League campaign with four games that could make or break their season.
Firstly they travel to Anfield on Sunday to take on fierce rivals Liverpool before home clashes against Southampton and Stoke City which is followed by a trip to Chelsea.
Van Gaal's predecessor David Moyes was relieved of his duties in the 2013/14 when it became mathematically impossible for the side to qualify for the Champions League - shortly after being knocked out of the competition. It's clear from this action that Champions League football every season is a minimum requirement at Old Trafford.
Last season United were facing a similar set of important fixtures, all be it later on in the campaign when they faced Tottenham and Liverpool in consecutive weeks in March - where wins in both games effectively sealed a place in the top four.
The club should be heartened by that experience that they can turn it on for the big games, but having experienced one barren run very recently, and conceded late on against Newcastle United this week, the situation perhaps feels that little more delicate.