The two clubs will clash in the League One play-off final at Wembley on Saturday. Speed, found hanged in his garage in November last year aged 42, spent two years as a player at Bramall Lane before replacing Kevin Blackwell as manager in August 2010. He left the club to take charge of Wales four months later, but left a big impression on the playing staff.
"The club's had a great season and we want to get promoted, but we're constantly thinking of Speedo," said Montgomery, at 33 the longest-serving player at Bramall Lane.
"Obviously he was manager of the club and if he was watching he would be desperate for us to get back to the Championship, so hopefully we can do it for him, do it for ourselves, for the fans and the current manager.
"We're all geared to get back to the Championship and missing out on the last day of the season to Sheffield Wednesday was a big blow, but we've got a good group of lads and we showed real resilience against Stevenage.
"That was a tough game to come through because they're a good strong side, but now we're just hoping it's going to be a nice summer.