Marco Silva’s Everton side and Brendan Rodgers’ Leicester City team are two of the teams pushing to break into the Premier League’s top six.
Fraser has under a year left on his contract at Bournemouth, and he has been linked with some of the Premier League’s top six.
But Sherwood thinks that a move to Everton or Leicester would suit the winger down to the ground.
He said: “It’s important for him to go somewhere and not have two years off.
“The next move for him, and no disrespect to Bournemouth, is one just underneath [the top six]. Like a Leicester or an Everton. And then he’s still young enough to make that next step.”
Whether Everton or Leicester will make a move for Fraser, if he doesn’t pen a new contract at Bournemouth, remains to be seen.
On a free transfer he could present Marco Silva’s or Brendan Rodgers’ sides with an excellent value for money addition.
There are question marks over whether Everton would have a use for Fraser though, after the addition of Alex Iwobi.
Everton have used a 4-2-2-2 formation at times this season, with Richarlison and Iwobi appearing first choices to play in the wide roles.
Leicester, meanwhile, may have more use for Fraser.
However, with the likes of Harvey Barnes, Demarai Gray and Marc Albrighton there would be no guarantees that Fraser, who was valued at £25 million (Daily Mail) over the summer, would be a permanent starter at the King Power Stadium either.
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