The youngster, how is only 18, is out of contract in the summer and can walk away as a free agent.
Cummings scored his fifth goal in five UEFA Youth League matches against Club Brugge last week.
Per The Mail, Brentford, Wolves, Fulham, Ipswich, Sunderland and Burnley are all chasing his signature.
While Celtic do want to hold onto the player, they are not rushing him into the first team.
“It’s your mentality. It’s your professionalism. All these things, alongside ability, are what get you the opportunity,” said manager Brendan Rodgers recently.
“In terms of Daniel’s output, his goals in his games, he’s done very well.
“But, like I say, there’s a lot of factors I consider when bringing in a young player. Ability is the first thing I look at, but your attitude and application are just as important.”
- Get breaking football news faster with the new Tribal Football app! Download now on iOS and Android to stay ahead of all the latest transfers and football updates. Download now: App Store, Google Play