Cleverley scored a late header to give Everton a 1-0 win at Newcastle United with his first goal for the club since making a permanent switch from Manchester United.
"I know as players you’re biased to your own team-mates, but I think it’s only right that I speak on behalf of a lot of the lads in our dressing room when I say Tom should be in the England squad - on current form at least," Stones told Everton TV .
"He’s playing terrifically well. Sometimes players don’t get too many chances to get back into the squad but I’m sure he would be delighted to."
The former Manchester United midfielder joined Everton in July and has not played for England since November 2013 in a 1-0 loss against Germany.
Stones said Cleverley's goal was well deserved after a string of good performances.
"He caught one sweet early doors and did the same against Crystal Palace, so maybe it’s a sign of things to come but he has definitely deserved it," added Stones.
"It took a lifetime to go in but thankfully it got there in the end.
"He feels like an Everton player. He loves everything about the club - the training, the fans and he’s just fitted in so well. He’s a top lad and the goal should top that off for Christmas."
Stones said the late winner made for a sweet Christmas present for the away fans, tucked away high in the stands of St. James' Park.
"A last-minute winner the day after Christmas - we couldn’t have planned it any better really as a great present for the fans," Stones said.
"We know they were sitting so high up in the stands but we could hear them all game. We’re so pleased and hope they are too."