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The Grecians chief was at last weekend's FA Trophy tie between the Shots and Grays Athletic to run the rule over the former Yeovil Town star.
Inglethorpe has made no secret of his need to recruit a winger following the departure of Tony Scully to Crawley Town last month.
And with the January transfer window opening for business in less than two weeks' time, the City boss is stepping up his efforts to swell the ranks for the second half of the season.
Bracknell born Crittenden started out his career as a trainee at Premiership champions Chelsea before joining City's Devon rivals Plymouth Argyle on a short loan spell.
The 27-year-old then spent four years at Yeovil, helping to guide them into the Football League, only to find himself released at the end of the 2003/04 campaign.
He joined the Shots at the beginning of last season and has made 48 appearances for the Shots, scoring 10 goals.
With his contract up at the end of the season, the winger has become the subject of interest from other clubs desperate to lure fresh talent in the transfer window with City looking to head the hunt.