Gleeson, 32, was a close season capture following the end of his two-year drugs ban, and he is likely to be a key part of new coach Brian Noble’s plans. The pair previously worked together in the Great Britain set-up.
Former Souths back-rower McPherson joined the Reds following the collapse of the Crusaders franchise, who he had originally signed for.
Gleeson said: “I am very happy at Salford and really feel this is the place to be because of what is likely to happen here in the next few years.
“The club has so much potential and I am enjoying my rugby.”