The 21-year-old striker posted a picture of himself as pre-season training began at Everton yesterday, but his future at the Premier league club is uncertain with speculation that manager Frank Lampard is looking to sell him rather than loan him out again.
Simms impressed on-loan at Hearts in the second half of last season, scoring seven goals in 20 appearances to Robbie Neilson's side qualify for Europe and reach the Scottish Cup final.
The Hearts boss is keen to be reunited with the Everton striker, who is attracting interest from Milwall and a host of other English Championship clubs. The Scottish Sun has reported that Rangers are also tracking the player with interest.
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Everton are understood to value the Englishman at around £500,000 and while that fee could be met by Hearts, the striker’s wage demands could prove prohibitive.
Taking the player back on loan is another option for Hearts if a transfer elsewhere doesn’t materialise, but that is not something that would happen until late in the transfer window.
Neilson has previously admitted that Hearts will struggle to bring Simms back for the season ahead.
Speaking last month, he said: “I’d love to get him back and we’re trying to get him back, but if I’m being brutally honest, I don’t think we’ll get him back.
“There’s a lot of Championship teams in England that have contacted me asking about him. Obviously I’ve said he’s been terrible!
"There’s a lot of teams that have been watching him and want to take him, so that’s where we are at the moment. We bring these guys in, give them a platform and try to progress them. Then if they do well, they move on again.
“We’d love to do it but I just don’t see it happening. I know we have (European football) but what they have is finances. We just made a small contribution to his wage. If he goes to the Championship. Someone can pay a much larger contribution or all of his salary. That’s what I can see happening.”