And he has now captured Glennon on a deal until the end of the season, with the 31-year-old set to go straight into the squad for Saturday's home game against Notts County.
McCall said: "We're delighted to bring Matt to the club, he's a goalkeeper with a great pedigree and a good track record.
"He brings lots of experience with him, which is exactly what we were after, and he is also very vocal and a good talker, which is important.
"Once it became clear that Easty was going back, Matt was our number one target. We have had a lot of goalkeepers put to us over the last few weeks, but Matt fits the bill perfectly."
Glennon added on the club's official website: "I have had opportunities to join teams in Huddersfield's division, but they had no aspirations of promotion.
"I would rather be playing my games at somewhere that has the hope of achieving something.
"I want to get some games and play some matches that's for sure."