The Italian – who turns 42 on Tuesday – is being considered by Lerner after his impressive three month spell at Chelsea that saw him deliver the FA Cup and Champions League to Stamford Bridge.
However it looks unlikely that Roman Abramovich will offer him a deal to take the job on a full time basis.
That has alerted Lerner who is set to step up his search for McLeish’s replacement this week and is reportedly set to move for the former Blues midfielder.
The American is impressed by the way Di Matteo picked up the reins from Andre Villas-Boas repairing a fractured dressing room and believes he could have a similar effect at Villa Park.
But former boss Atkinson believes it’s imperative that the 50-year-old millionaire needs to loosen his purse strings and allow his next manager to rebuild the Villa squad.
“This is the probably the most threadbare Villa side I can remember in the Premier League and it’s obvious they need players.” Atkinson said. “I felt sorry for Alex McLeish because you can only work with the tools you’ve got and the squad he had just wasn’t good enough.
“They need at least three top-of-the-range players to climb the table and lift the crowd. Those supporters were brought up on a bit of glamour and Villa need stars get them excited again.
He added: “Villa is a magnificent club, with a great fanbase and fantastic training facilities. You’d expect any manager offered the job to jump at it.
“But he has to be given money to invest in the team. They are lightweight in midfield and certainly need more quality there. Unless the new boss can spend, it could be no better next season.”
The 73-year-old spent three years with Villa, almost guiding them to the Premier League title in 1993 has challenged Lerner to vanquish their reputation as a ‘selling club’.
Atkinson said: “Over the last couple of years they’ve lost something like seven top players – and most of them are or would be in the England squad.
“They simply haven’t replaced the likes of James Milner, Gareth Barry, Stewart Downing and Ashley Young. Gary Cahill is ex-Villa, and Kyle Walker had a spell at the club too.
“Building a top team isn’t rocket science. You have to have quality players. We had good players back in 1992-93 and we were close to being champions.
“For Villa to become anything like a top team again they have to bring in players capable of taking on and beating the best in the Premier League.”