The 20-year-old is a graduate of the famed Boro academy and has captained their youth side in recent years.
He finished last season on loan at Yeovil and helped the club to claim their momentous promotion to the Championship.
Now the Glovers are keen on taking Dolan on a permanent deal, but he has a year left on his contract with Boro, who are now considering their options in regard to the player.
A host of League One and Two clubs, including Hartlepool United - now managed by former Boro coach Colin Cooper, who knows the player well - are also keen on signing him.
But the player is believed to be keen on getting the chance of regular first-team football in the Championship, which Yeovil would present him with.
"I'm happy to take Matty Dolan if he's a free agent and now it's up to Middlesbrough," manager Gary Johnson said earlier this month.
"They have done brilliant for us because they didn't charge us for the last loan, although we knew he wouldn't be fit until the final anyway.
"We owe them for 15 minutes last month. He was unlucky because he didn't play many games. We'll take him but only if Middlesbrough will release him."