"It's actually a two-way trial," boss Coppell told the club's website. "We're looking at him as an out-of-contract player and he's looking for a club."
Defender Rosenior helped City lift the LDV Vans Trophy in 2003 before joining Fulham three months later.
Coppell signed him for Reading in the summer of 2007 but the player spent much of last season on loan at Ipswich.
"I know Liam believes there are some Premier League clubs looking at him and he needs to be playing games for fitness," added the manager.
"We're looking for players so it's a mutually beneficial arrangement."