Liverpool are seeking to organise a friendly with Blackburn Rovers in the coming days.
Jurgen Klopp's side are set to resume competitive action in the Merseyside Derby against Everton on June 21.
The Lancashire Telegraph says Tony Mowbray's squad moved in to Phase Two of their return to training on Thursday, which permitted tackling and groups of up to 10, and they now look set to host the Reds in a practice match later next week.
Both Premier League and EFL clubs have been given the green light to host friendlies this week, albeit under strict rules which would see teams only able to travel within a 90-minute distance, and that the players would travel alone.