The Premier League outfit are said to have eight rooms designed for players to sleep at within their training complex at Carrington.
According to United's head of fitness Tony Strudwick, there are concerns that players cannot sleep as easy when they have young children. Rooney has two sons Kai, four, and 11-month-old Klay.
"You find that players who have young children get a slightly lower quality of sleep when those children are very young and that can affect performance," the Daily Star quotes Strudwick as saying. "We have an extensive monitoring and recording process in place."
In the Premier League, United are currently seventh in the table, nine points behind fourth-placed Everton.