The Red Devils sacked Jose Mourinho yesterday and placed Ole Gunnar Solskjaer in charge for the remainder of the campaign.
United will now conduct a search for a permanent boss but the club view Tottenham manager Mauricio Pochettino as their ‘ideal’ candidate.
Pochettino, though, is in two minds about leaving Spurs and United will need a decision before the season finishes in order to ensure their man is in place in time.
Conte left Chelsea at the end of last season after the Blues beat United 1-0 in the FA Cup final at Wembley.
The Italian guided Chelsea to the Premier League title during his first season in charge and Conte is still diving his time between London and his homeland, Italy.
Conte turned down the chance to take charge of Real Madrid for the remainder of the season following Julen Lopetegui and is only interested in a permanent role.
The 49-year-old feels he was wrongly sacked at Chelsea and believes he has unfinished business in England.
United are expected to target Pochettino as their first choice but the Telegraph claim Conte is interested if they fail to land the Argentine.