The former Shrewsbury and Crewe ace, who can operate on the wing or in attack, is a free-agent after terminating his three-year deal at the Blues in order to stay in the Football League.
Several other Football League clubs are also rumoured to be keeping tabs on the Liverpool-born ace, who scored 18 times for Mark Wright's relegated side last year.
Allen, who held talks with Lowe earlier this week, told The Gloucestershire Citizen: "Ryan is an excellent player who I have known about for many years and a player I've tried to sign before.
"He scored 18 goals for a relegated team last year. I've watched him a number of times and we could certainly fit him in.
"I'm hopeful, but a number of other clubs are interested in him, so we'll have to see how it progresses. The fact that he came down to meet us is important and I think he liked what he saw at Cheltenham."