The process to explore “strategic alternatives” for United began in November, when the Glazer family, who bought the club for £790m in 2005, announced they were considering selling.
The Americans have established a valuation of £5-6bn.
As outlined at the beginning of the process, interested parties have been asked to submit a third round of proposals by the end of this month.
It is not clear whether the Glazer family will sell the club or retain control.
However, confirmation this week that Old Trafford will not host matches at Euro 2028 despite having the largest capacity of any ground in England apart from Wembley has once again brought into focus the amount required to modernise the ground.
It is estimated that cost would be at least £1bn, with some arguing a better option would be to build a new ground close to the current one, as Tottenham decided to do.
Carlyle has declined to comment on its interest in the process.
