The Sunday Mirror says Liverpool have now offered the Stockport-born teenager a week-long trial with a view to a permanent move that could net £200,000 in compensation for the League Two club.
Rochdale assistant boss Dave Flitcroft said: "Matty has great leadership qualities and a fantastic attitude and I can honestly say I have never seen a young player so focused.
"To see a story like this unfold in front of your eyes is fantastic. When he has trained with the first-team, the senior professionals have given their all to help his improvement.
"I feel sure that Matty is going to be a real player who goes on to play at a very high level."