The Red Devils boss is said to have contacted the striker about a move to Manchester this summer.
The 20-year-old currently plays for RB Leipzig but has no future with the Bundesliga side having spent the second half of last season at former club Ajax.
He joined the club from the Dutch champions on a free transfer in 2021 but returned to Holland earlier this year, where he scored seven goals in 11 games under Ten Hag.
"I told [Leipzig] that I would prefer staying with Ajax," Brobbey told Dutch newspaper Algemeen Dagblad last month.
But now Man United could be set to hijack the deal, with Leipzig said to be looking for around £17million for the youngster, though it is understood that he could go for around £13m.
According to The Times, Ten Hag phoned Brobbey in an attempt to convince him to move to the Red Devils this summer.
The Dutch boss has been linked with numerous players he has previously worked with including Frenkie de Jong, Lisandro Martinez, and Antony.
After the departure of Edinson Cavani and reports that Cristiano Ronaldo wants to leave, Man United may need to strengthen their attacking department this summer.
The club confirmed that Ronaldo is not in their squad for pre-season games in Thailand and Australia.
They say he is not in the 31-man group for their pre-season tour and 'has been granted additional time off to deal with a family issue'.