The Glazers and executive vice-chairman Ed Woodward accept that Solskjaer's squad has been left short in midfield and up front after the summer departures of Romelu Lukaku, Alexis Sanchez and Ander Herrera.
United have also reportedly opened talks with Barcelona to discuss a potential deal for Ivan Rakitic.
According to the latest reports, Premier League giants Manchester United were close to signing French superstar Antione Griezmann in the summer transfer window until Barcelona made a decision to swoop in for the playmaker.
The United boss has only Marcus Rashford and Anthony Martial, both of whom have had injury issues, as established No 9s with 17-year-old Mason Greenwood his only back-up to the duo.
But while 33-year-old Mandzukic would be available at a low fee, with United unwilling to pay over the odds for their manager's targets, they want him to lower the wages he wants to join the club.
Mandzukic has dropped down the pecking order in Turin and is but to characteristic in any competitions this season beneath Maurizio Sarri.
Mandzukic has enjoyed four excellent years at Juventus since arriving from Atletico Madrid in 2015, winning four straight Italian league titles and scoring 44 goals in 162 appearances.
From their opening eight games in the Premier League, United have mustered up just nine-points and are 12th in the table, 15 points behind log leaders Liverpool.
But the Norwegian coach is not under pressure from the United hierarchy, who remain strong in their belief that the former striker is the man to end the club's post-Sir Alex Ferguson gloom.