Oliver, the 2012 player of the year, has been restricted to just four appearances this term, and, along with out of favour Connell, has been deemed surplus to requirements.
City boss Phil Parkinson said: “We’re just waiting for the phone to ring on those players.
“There were one or two clubs looking at Luke Oliver, one from the Scottish Premier and another from the Conference were interested in him. Alan’s also had a couple of inquiries.
“They both know the situation. Olly has been terrific for the club but because of injuries he’s probably at the stage where he needs to go out and play now.
“We are trying to get something sorted and get him some games. But it’s got to be something he wants to do.”
Partick Thistle were thought to be the club north of the border who sounded out Oliver before they signed St Mirren centre half Lee Mair.