It was reported on Wednesday (MEN) that 21-year-old defender Stones will be the subject of a bidding war between Manchester United and Manchester City, whereas striker Lukaku, 23, confirmed he'd be leaving the Merseyside outfit, via Sky Sports.
Stones, in particular, was the subject of intense interest from Chelsea last summer, with Jose Mourinho - thought to be on the brink of becoming United manager - having three bids knocked back, the most expensive of which was £37 million
The Toffees currently have no manager following the sacking of Roberto Martinez earlier this month, after Everton finished 11th in the Premier League, but there is less speculation surrounding Barkley's future at Goodison Park.
The midfielder is one of England's most promising young talents, one who has been repeatedly linked with a move to Man City, but Parlour, speaking to Alan Brazil's podcast, says that the 22-year-old might well stay.
"I think Chelsea will definitely be back in for him," Parlour said of Stones. "They'll be looking at the Everton situation - no manager at the moment - and Lukaku looks as if he's off as well.
"I think Stones and Lukaku will be the ones who leave. Barkley maybe stays. I think he might stay."
Keeping Barkley is a must. Losing Lukaku and Stones would leave their next manager with a lot of money in which to rebuild Everton, and prospective targets would be more receptive toward a switch if Barkley was retained, perhaps.