Dean Smith was sacked as Villa boss after five consecutive Premier League defeats left them side sinking towards the bottom three.
The club's most recent loss against Southampton ended Smith's three-year stint at his boyhood club, having taken the side from 14th in the Championship back to mid-table in the top flight.
Villa have backed Smith heavily in the transfer market with more than £300million invested over the past three summers, but they have been unhappy with the lack of progress this season.
Smith lost star player Jack Grealish to Manchester City for a league-record £100m during the summer, but the head coach was boosted by the arrivals of Emi Buendia, Leon Bailey and Danny Ings.
They haven't hit the ground running so far this season, and Villa are now on the lookout for an upgrade in the dugout, with Premier League legend Gerrard the current bookies' favourite.
However, Gerrard is tied down to Scottish Premiership champions Rangers after guiding them to a first league title in a decade, and good friend Murphy believes a switch is unlikely.
"I would be very surprised, very surprised, if he was to leave Rangers to go to Villa," the talkSPORT host said.
"Not that Villa's not a great club, but there's only so far you can take Villa, the ceiling is low."
Murphy was challenged by talkSPORT host Jim White, who believes Villa have shown their aspirations with a hefty net spend since returning to the Premier League.
"It doesn't matter what they've spent, I'm talking about from Gerrard's position," Murphy replied.
"If you ask me a question about his mentality, I would suggest that he wants to be at the top of the tree in management in terms of competing for winning leagues, Champions Leagues and European trophies.
"At Rangers he's trying to win titles again, he's in the Europa League, and I think, as I've said before, his ultimate ambition would be to manage Liverpool. Is there another stepping stone between Rangers and Liverpool? I'm not sure there is."
Since retiring as a player following two seasons in MLS with LA Galaxy, Gerrard underwent a spell at Liverpool's academy before taking the reins at faltering giants Rangers.
The 41-year-old's stock has risen considerably as he continues to challenge Celtic, with many seeing his ultimate goal being a return to Liverpool in the future.
But in Murphy's eyes it would have to be a hard sell from Villa who would have to offer attractive investment to help challenge in an increasingly competitive Premier League.
He explained: "I suppose it would come down to, and this is where we don't know, if Stevie was presented the opportunity by Villa, what their vision is and what would their be funds?
"Would there be an autonomy that he would have to bring in transfers? All those things matter to a manager
"If they're really serious about that and they present that to a manager, whether that be Stevie or anyone else, of course it's more appealing, so we'll have to wait and see on that.
"Never say never in football. Stevie's ambition, I don't know. It would be a challenge going into the Premier League and managing Villa with the competition being the way that it is at the moment.
"You're not just looking at the top four, you're looking at Leicester, Tottenham are now going hard with [Antonio] Conte, Arsenal have turned the corner, it's very competitive to get in that top eight, top nine."
Aston Villa legend and fellow talkSPORT host Gabby Agbonlahor has backed Gerrard for the job, singling him out as the ideal candidate.
"I'd love him to come," Agbonlahor said. "Watching his passion on the side with Rangers, watching how Rangers play football, I think it would be a great signing for Aston Villa.
"I feel as well for Rangers, what more can he do with them. He's won the title after such a long time of not winning it and I feel the time is right now to come to Aston Villa.
"I feel the players will respect Steven Gerrard - one of the best Premier League players ever.
"I would be buzzing with that signing.
"Steven Gerrard has been named for most of the jobs going, so he has to take one sooner or later."