The 30-year-old's agent, Willie McKay, revealed earlier on Wednesday that his client "would love" to join the Toffees, and is willing to take a pay cut to force through a move to Goodison Park.
|22/1||Everton are 22/1 with Coral to finish in the top four
"I think they have already got a kitman," Southall told talkSPORT. "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?
"I would rather [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 spent last season on loan at Ligue 1 outfit Marseille, but returned to parent club QPR this summer.