Telford are understood to have been in talks with Paul Carden, manager of step three Warrington Town, after the Yellows confirmed yesterday they had granted their boss permission.
The new man in charge will be confirmed at 1pm.
For interim pair Greene and Meechan, yesterday's 2-1 home defeat to leaders AFC Fylde was a final outing of a difficult eight-game tenure, where their position remained in the air throughout.
Greene led the Bucks to a single win and two draws from that period. Yesterday's reverse was a third defeat on the spin for the boss, who claimed he wanted to take the job on full-time.
Telford dropped to bottom of National League North with yesterday's defeat. The club board maintained throughout Greene's six-week tenure – which was called 'semi-permanent' by the boss himself in recent days – they were on the lookout for a permanent option.
Initial results and performances suggested an improvement following Gavin Cowan's dismissal but it is thought recent defeats that have seen the Bucks plummet further have accelerated the club's search.
Both during the week and following yesterday's visit of the Coasters, the former Boston boss said he required clarity on his position and admitted it could have been his last game in charge.
And the duo have now left the New Bucks Head, with a statement due on the new management team set to be confirmed at 1pm.
Liverpool-born Carden, 42, enjoyed a playing career that spanned some 16 years and included lengthy spells at Chester and Cambridge.
He held caretaker roles at both Cambridge and Tranmere as well as a brief stint in charge of Southport for less than a year in 2015, where he secured the club's status in what is now the National League.
He has been in charge of Warrington since October 2016, where the Yellows have recorded some impressive finishes in the Northern Premier League Premier.
Carden guided his club to positions of 10th, then back-to-back third places in his first three seasons.
Warrington lost to Grantham in the play-off semi-final of 2017/18 but a year later saw off Nantwich Town and won the final away at South Shields before being denied promotion against King's Lynn Town, the Southern League play-off winners.
The Yellows have looked well placed in each of the last two seasons, which were curtailed early due to Covid-19.
And following yesterday's 2-2 draw against Mickelover Sports, Carden's men sat sixth.