Last season's Championship top assister was handed an England under 21 call-up, before being added to their squad for this summer's European Championship.
It was predicted Fellows would attract interest this summer, as he has done in previous windows.
And that seems to be the case, with Leeds and Everton both linked this week with potential moves for the wide man.
It comes after Albion saw Mikey Johnston remain at the club after a potential £5m move to Flamengo was called off.
It remains to be seen whether Albion may have their hand forced to sell if a bid comes in - but one former Baggies forward believes leaving Albion now would not be beneficial for Fellows.
Speaking to football betting site talkSPORTBET - Don Goodman issued a warning to Fellows, and believes he would be best served staying at The Hawthorns.
And he has used a comparison with another player who played in the Premier League last season.
He said: "14 assists last season in the Championship is very impressive, along with four goals, but there's just a part of me that wonders if at 21, a little bit like the answer I gave you about Omari Hutchinson, whether he's quite ready yet because there were times last season where he was left out of the West Bromwich Albion starting XI, so there are still elements of doubt.
“Last year was a real breakout season for his development. So for me, a little bit like Hutchinson, Tom Fellows would probably be best served by another season in the Championship with West Bromwich Albion.
“If he were to go to the Premier League, it's hard for me to see him playing week in, week out and that would just halt his development slightly.
“It'll be interesting if West Brom get a massive offer and one they can't turn down - then he’ll be off but at the minute I think personally he'd be best served by spending another season at West Brom.”