The interim boss has been in his New Bucks Head role for more than three weeks now following Gavin Cowan’s exit.
Telford’s week on the field has been disrupted by Covid-19 cases with opposition. Tuesday’s home clash with Guiseley was called off and Saturday’s visit of Curzon Ashton is in doubt.
The club are believed to be keen to play for revenue streams and looked into arranging another fixture.
However, Greene looks set for a continued run in the Telford dugout as other candidates previously in the running are understood not to have been approached or revisited. Greene has so far overseen four games.
If the Curzon clash is off, Telford next travel to Bradford PA on Saturday week.