Born in Stockport, Greater Manchester, Glennon started as a trainee at Bolton Wanderers, but could not break into the first-team and after unsuccessful loan spells at First Division clubs Port Vale and Stockport County, he finally made his professional debut on loan at Second Division side Bristol Rovers in a 0–0 draw with Wigan Athletic at the Memorial Stadium on 16 September 2000, and was described as "impressive" after making "important saves from Kevin Nicholls and Simon Haworth".

Manager Paul Simpson guided United to promotion at the first attempt as play-off winners in 2005 with a 1–0 win over Stevenage Borough at the Britannia Stadium.

[12] He moved on to Scottish First Division side St Johnstone in January 2006 after manager Owen Coyle released back-up goalkeeper Mark Paston.

[13] At St Johnstone he scored his only senior goal, as a desperate last-minute attempt to equalise paid off in a 2–2 draw at Ross County on 11 March.

[14] Coyle offered Glennon a contract to stay at McDiarmid Park, but he instead chose to return south of the border to sign with Peter Jackson's Huddersfield Town in June 2006.

[18] Manager Andy Ritchie said that he would appeal the red card after striker Leon Clarke admitted that he had slipped rather than been fouled by Glennon.

[20] However, he did not feature under new manager Lee Clark, who took charge in December 2008 and kept faith in teenager Alex Smithies, and Glennon had his contract terminated in January 2010.

[21] He then joined League Two side Bradford City on a deal until the end of the 2009–10 season after manager Stuart McCall needed a replacement for departed loanee goalkeeper Simon Eastwood.

[29] He played 51 matches in the 2012–13 campaign, and kept a clean sheet in the Conference North play-off final, as promotion was secured with a 1–0 victory over Brackley Town.

[31] He missed just one league game in the 2013–14 season as he helped the club to secure a play-off spot, where they were beaten by Cambridge United at the semi-final stage.

[35] He again came out of retirement in February 2017, to play one game for AFC Emley in a Northern Counties East League Division One against Brigg Town after regular goalkeeper Graham McLachlan picked up a suspension.