High-placed sources at Old Trafford have confirmed their interest in a player who is also being strongly pursued by fierce rivals Liverpool.
The futures of Robin Van Persie and Radamel Falcao are uncertain and Van Gaal has put the 22-year-old Englishman on his list of targets.
United have held talks with Burnley and through a loophole in Premier League regulations are able to agree a fee and pre-contract with the player to ensure a transfer in the summer.
Liverpool manager Brendan Rodgers tried to sign the striker in January, but Burnley were intent on keeping him until the end of the campaign.
Ings is out of contract in the summer but, due to his age, Burnley would be owed a fee set by a tribunal of around £5million if he joined an English club.
However, under Premier League Rule U8 domestic clubs are able to agree terms with the club and player who would then move when their contract expires.
Ings has become one of the most sought-after strikers in Europe. If United are successful they would beat former manager David Moyes, who is keen to bring the 22-year-old to Real Sociedad, to the signing. Tottenham and Manchester City are also interested.
Ings has scored nine goals so far in his first season in the Premier League and United consider him to be a future England international.
Van Gaal was particularly impressed by Ings’ performance against United at Old Trafford in February when he scored in Burnley’s 3-1 defeat.
Van Persie, 31, has struggled with injuries this season and the loan of Falcao, 29, from Monaco has produced only four goals.
United are also interested in signing PSV forward Memphis Depay, Southampton right back Nathaniel Clyne and Dortmund centre back Mats Hummels.