The Italian is the frontrunner for the job if United change their position on Solskjaer’s future.
Solskjaer has been given three games to save his job at Old Trafford and they are against Tottenham, Atalanta and Manchester City.
If the 48-year-old oversees more damaging results, he could be out of the job by the next international break.
Conte is being considered as the “right solution” if that happens.
However, the 52-year-old would insist on bringing a trusted defender with him. The report claims a deal may well hinge on the “purchase of a loyal player from Inter as early as January”.
De Vrij made 32 appearances, as Inter won the Scudetto under Conte last season.
The Dutch defender is seen as “ideal for guiding the transition from a four-man defence to a three-man defence”.