BristolLive had previously reported that the player was set for a switch to the Riverside despite signing a new deal in March of this year. And Sky Sports reporter Keith Downie has since claimed that the player is undergoing routine physical checks ahead of the imminent deal.
"Aden Flint currently undergoing a medical at Middlesbrough after fee was agreed with Bristol City," Downie reported via his Twitter account on Tuesday. "The defender will cost upwards of £5m."
Bristol are understood to have been reluctant to lose Flint this summer, yet a reported £5m has seen Boro steal a march on other suitors to land their man.
Tony Pulis is also said to be a huge admirer of the towering, 6ft 6in centre-back, who scored nine goals for his side last season, also helping them to the semi final of the Carabao Cup.
Flint, a fan favourite at Bristol, joined the club five years ago, coming in as a summer signing from Swindon Town for £300,000 in 2013.
He will leave the Robins having helped them win League One and the Football League Trophy in 2015.