Boro have been tracking the forward for months but are assessing their options as Neil Warnock looks to bring three new strikers to the Riverside.
Diedhiou finished as City’s top scorer during the 2018/19 and 19/20 seasons, scoring 12 and 13 goals respectively.
Yet, despite impressing during the Robins’ 3-1 win over Boro in February, he has netted just eight league goals this campaign.
City announced on Friday morning they would be releasing 12 players, including Diedhiou as well as former Aston Villa pair Nathan Baker and Henri Lansbury.
Manager Nigel Pearson said: “I have spoken with each departing player and wish them all well in the nextstage of their careers.
“We are entering into a significant transition period for the club and central to that is deciding which players can take this club forward. The first element of that is largely done and now it’s about looking forward to whom we can bring in as we build towards next season.”
Diedhiou was reportedly offered a new deal at City earlier in the campaign but the two parties couldn’t agree new terms at Ashton Gate.
Boro’s interest will depend on the player’s wage demands and despite interest, it’s understood that talks regarding a move to Teesside are yet to reach advanced stages.
Diedhiou has also been linked with a move abroad and missed City’s last three games of the season with a knee injury.
The striker’s last goals came against Boro at the Riverside when he bagged a brace.