Southall, who in his playing career was far from the consummate athlete, likened Barton to the fictional character played by Tom Hanks' in the 1994 film of the same name.
The Huyton-born player has said he would sacrifice a large proportion of his reported £70,000-a-week wages to play for his boyhood club but Southall believes it would be a mistake.
Asked whether he thought Barton would be a good signing the outspoken former Wales international said: "I think they have already got a kitman.
"What is he going to add to Everton? He might be a half-decent player at times but, if he was that good, Harry Redknapp would be begging him to stay at QPR.
"I don't see how he will fit into Everton's style of play. He ain't the best passer in the world.
"Yes he is fit and runs up and down all day but Forrest Gump did that as well didn't he?"
Southall added on talkSPORT: "I would rather he (Martinez) got in a young lad who is probably on less money and a better prospect in the long run so they have got until January to bed him in and see what he is like.
"A 30-year-old at Everton? I was hoping they were past that, unless he was a current international."
Barton, who today tweeted 'Once a blue...', spent last season on loan at Marseille but appears to have no future at Loftus Road after their relegation to the Championship.
His salary seems to have put off the French club from making a move to sign him permanently and agent Willie McKay is exploring other options in an attempt to find a new club.
"Obviously his package with QPR is pretty big for Marseille's terms really," said McKay.
"Joey said there was only one club he would make a sacrifice for and it would be Everton and I made that call to Martinez.
"That is the club he loves. I have approached them and said Joey would love to have Everton on his CV.
"Fair play to him he said he would lose money to go to Everton - and not many professionals would do that."
McKay claims Martinez, who is in the market for a central midfielder, is an admirer of Barton.
"Roberto Martinez said he likes him as a player and he also spoke to Graeme Jones, who loves him as a player," he added.
"Anything can happen in football. It could happen."
Martinez and the rest of the Everton squad are currently in San Francisco where they will kick-off their pre-season games in the United States tonight against Juventus in the International Champions Cup.
Everton will not comment on speculation about players at other clubs.