The 21-year-old's long-term future at Stamford Bridge remains unclear ahead of his return to preseason training July 30, although Everton has agreed to two deals for the striker.
Sources told Goal UK on Sunday morning that Roberto Martinez's side has agreed to two deals - one loan and the other a 25 million euro permanent move - with Chelsea for the Belgium international.
Lukaku scored 16 goals during his season-long loan spell with Everton last season, and Martinez already has expressed his desire to bring the 21-year-old back to the club.
"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 brilliantly for us last season. Gareth Barry has signed permanently now which is fantastic, and hopefully Lukaku will as well," Atkins continued. "I know the manager would like him back 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."