Saturday's 4-2 defeat to Leicester City piled the pressure on Solskjaer, with the Red Devils collecting just one point from their last three Premier League matches, while they have won just one of their last five matches in all competitions.
Man United allegedly have no plans to sack the 48-year-old, but the former striker will come under pressure if the team's poor run of form continues.
According to The Mirror, Conte is regarded as the leading candidate to replace Solskjaer, with the Italian still available, having not taken a job since leaving Inter Milan.
The 51-year-old, who was linked with Tottenham Hotspur over the summer, won the Premier League and FA Cup during his time at Chelsea, while he has lifted four Serie A titles as a manager, three with Juventus and one with Inter.
Man United are back in action against Atalanta BC in the Champions League on Wednesday night before facing Liverpool in the Premier League next weekend. body check tags ::