Barkley has been strongly linked with a move away from Everton this summer, and is widely expected to move on.
And Lampard believes that the England international’s career will benefit from a move away from Goodison Park.
“While it does look like he's going to leave now, he does need to go to a club where he can fulfill that talent," the Chelsea legend said.
“It's all there, but he probably just needs to get a bit more out of himself. He's at a young age and it seems that he wants to move.
“If he comes to a team like Chelsea or Tottenham, the players around him will help him improve because he'll see what it takes to go to the next level."
It appears that Ronald Koeman has some doubts over Barkley, and the 23-year-old’s refusal to sign a new deal has put an end to his time at Everton.
Koeman confirmed earlier this summer that Barkley had played his last Everton game, although he seems to have relented more recently.
Everton’s asking price has not yet been met, and if Barkley doesn’t move, Koeman has suggested that the attacking midfielder could yet come back into his plans.
Tottenham are yet to make a signing so far this summer, but Pochettino has recently assured fans that new additions will be made.