The 18-year-old has reportedly requested £50,000-a-week to sign an extension with the club.
Solanke's current deal runs until the end of next season.
He's scored seven times in 24 games while on loan at Vitesse in Holland.
Arsenal are among the clubs believes the be monitoring his situation, but Chelsea keen to tie him down.
“The relevant people working as part of Dom’s development programme will sit down and discuss what is best for him once he has finished up at Vitesse Arnhem,” said youth coach Joe Edwards.
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“But he’s definitely one of the boys we’ve got high hopes for and, hopefully, whether it’s this coming season or further down the line, he’ll be one [who makes his mark at Chelsea].
"I think there are several who can. And we saw with Marcus Rashford at Manchester United that you won’t see properly what they can do until you put him in.”