Mbappe, who has scored four goals and provided four assists in 11 games for the Ligue 1 club this season, burst onto the world stage with Monaco last season.
Manchester United midfielder, Paul Pogba, scored twice as they defeated Fulham 3-0 on Saturday in the Premier League. His two goals against Claudio Ranieri's side saw him break his personal record for goal scoring in a season.
And following an unimpressive display from Pogba in Manchester United's 1-0 defeat to Barcelona, the 26-year-old Frenchman could be the one who gets left behind.
The 18-year-old, who has four international caps for his country, scored 27 goals and provided 17 assists in 59 appearances in all competitions for the Ligue 1 champions last season.
Pogba however impressed in the 5-1 win over Cardiff City last Saturday and in Solskjaer's first game in charge at Old Trafford on Boxing Day, as United eased to a 3-1 victory over Huddersfield Town.
"I will work even harder to come back stronger and hopefully before the end of the season. It's not over. Thank you all for your support, United we would stand!"
"The club is working on it and if there is any information we will communicate it as soon as possible." Messi's arrival in Ligue 1 would also mean PSG end their interest in signing Manchester United midfielder Paul Pogba.
Manchester United midfielder, Paul Pogba, has finally reacted to racist abuse aimed at him after the Red Devils' 1-1 draw with Wolves in the Premier League last Monday.
It is believed that a heavy defeat to Liverpool, could see Woodward and the owners the Glazers to pull the plug on the experiment, particularly with several key players including Paul Pogba, Luke Shaw, Anthony Martial, Victor Lindelof and Aaron
The Liverpool striker beat the likes of David de Gea, Paul Pogba, Marcus Rashford, Troy Deeney and Leroy Sane to win the award for a second month in a row.
Manchester United on Saturday, September 29, continued with their disappointing performance this season in the Premier League losing 1-3 against West Ham United.
"I would like to wish Chris, PaulandPaul - who have all worked extremely hard throughout their time here - every success for the future, and thank them on behalf of everyone at the club.
"Leicester have always been a team that bookies are wary of after their 5,000-1 Premier League winning season. "There's a lot of confidence around Leicester, they're the in-form team.