It is understood Villa have made the Gers manager their No. 1 target after sacking Dean Smith.
Having won the Scottish Premiership and inspired success in Europe, Gerrard is considered one of the most promising young managers around.
Many believe the Liverpool legend will follow Jurgen Klopp when the current Reds boss eventually moves on.
Villa are expected to approach Gerrard in the coming days and the 41-year-old is reportedly ready to listen.
While a Premier League job could be seen as the perfect stepping stone to Anfield, though, McCoist urges Gerrard to think twice.
Rangers' all-time leading goalscorer and former manager believes Gerrard could ruin his chances of managing Liverpool by taking the reins at Villa Park.
McCoist told the talkSPORT Breakfast: "He wants the Liverpool job, right? What if he goes to Aston Villa and it doesn't work out?
"He's got a better chance of success at Rangers than he has at Aston Villa, if he wants the Liverpool job.
"If he goes to Aston Villa and it doesn't work out, he won't get the Liverpool job."
Smith was sacked after a run of five straight defeats, despite getting Villa promoted and guiding the club to an 11th-place finish last season.
The decision is widely considered quite harsh - and McCoist believes Gerrard should be warned by Villa's ruthlessness.
He added: "I just think there are risks. I thought Dean Smith might have earned himself more time.
"I can understand it, but if I was Steven, I wouldn't do it. I'd stay where I am."
However, former England international Carlton Cole believes Gerrard to Villa would be a good fit.
He told talkSPORT: "I think he's ready to go there and it's the next stepping stone for him.
"I know if it doesn't work out it harms the end game of Liverpool.
"But he has to be able to take that risk and get better."