Boro officials have spent the last two days finalising their shortlist following Carrick’s departure as head coach on Wednesday.
Edwards is understood to feature prominently in the Teessiders’ thoughts, with formal interviews expected to take place next week.
The former Luton Town boss, who is currently out of work following his dismissal from Kenilworth Road in early January, worked with Boro head of football, Kieran Scott, and head of recruitment, Chris Jones, during his time at Wolves.
His availability is not just interesting Boro though, as he is also understood to feature on Bristol City’s shortlist of candidates as they look to replace Liam Manning, who left Ashton Gate last month in order to take over at Norwich City.
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Bristol City are at a similar stage of their recruitment process to Middlesbrough, with sources in the South-West claiming the Robins would ideally like to have their new boss in place by the end of next week.
Edwards could find himself being offered interviews with both Boro and Bristol City next week, potentially leaving him with a difficult decision to make if he was to be offered a position by both clubs.
In such a scenario, Boro would back themselves as a more attractive option than Bristol City, even though the Robins finished ahead of them and claimed a play-off position last season. Part of the reason Manning decided to leave Ashton Gate is understood to have been because he was questioning whether the finances were in place to take the club forward next season.
Boro chairman Steve Gibson will be investing in the current squad this summer with the aim of mounting a viable promotion push next term.
Steve Cooper remains a candidate for the Boro job, along with former midfielder Gary O’Neil. Sheffield Wednesday boss Danny Rohl is an option despite the need to pay compensation for his services, but former Boro assistant Robbie Keane is not being considered despite this week’s stories linking him with a return to Rockliffe Park
