Lerner will fly in from the United States to speak with McLeish along with chief executive Paul Faulkner in the aftermath of Sunday's 2-0 defeat at Norwich, which was described as "woeful" by the manager.
Sections of fans again called for the former Birmingham boss to be axed as Villa ended the campaign just two points clear of the bottom three.
McLeish has had to contend with slashing the wage bill, which he described as "astronomical", and has been deprived of several key players through injury or illness.
The likes of record signing Darren Bent, key defender Richard Dunne and skipper Stiliyan Petrov have been sidelined for lengthy spells and McLeish has had to put the accent on youth.
McLeish always stressed it would be a season of transition after replacing Gerard Houllier last summer, but it was still a surprise that Villa only made sure of survival last weekend.
Their tally of 38 points in finishing 16th is actually one less than when McLeish was relegated with Birmingham last campaign.
McLeish insisted after the 2-0 defeat at Carrow Road he was still the right man for the job and was aiming to rebuild the side.
But his future now depends on whether Lerner decides it is time to search for a fourth manager in less than two years or takes into account the difficult conditions McLeish has worked under.
Martin O'Neill quit in the summer of 2010 and Houllier had to leave Villa last summer on health grounds, which led to McLeish's controversial appointment after leaving Blues.
Source: PA
Source: PA