Atkins is the head of recruitment at Goodison Park.
"Romelu had a terrific season for Everton last year and I know everyone at the football club wants to see him back," Atkins told talkSPORT.
"Hopefully things can be sorted out, I think he's quite settled in his mind that he wants to come to Everton, and hopefully he'll be pulling on our blue shirt again next term.
"Our loan signings all did brilliant for us last season. Gareth Barry has signed permanently now which is fantastic, and hopefully Lukaku will as well.
"I know the manager would like back him at Everton and I'm sure if he comes he'll be a great asset and can help us get to that next level of European football."
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