Johnstone, who joined Villa in January, has started every match for the Lions since arriving in the Midlands. The Englishman's ninth loan spell since 2011 came to an end in Saturday's 1-1 draw with Brighton.
The Express reports that the Villa boss has already spoken to Mourinho over the phone but wants to elevate discussions when they meet.
It is believed the conversation will centre on whether Bruce would like to take Johnstone on a second loan spell or try to secure a permanent move.
Premier League clubs Everton and Bournemouth are also reported to be monitoring the situation.