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The player, who joined from Wolves for £750,000 three years ago, played a starring role in their 3-1 win at Wrexham and manager Brian Tinnion stated his wish to keep the Tynesider.
Tinnion said: "Tony met with the chairman (Steve Lansdowne) on Friday and the early signs are encouraging. We are going to put something in writing early next week in a bid to keep him at the club.
"Wigan will not allow us to extend the loan so if we want him, it has to be permanently but I will leave the money side of things to the chairman.
"Tony has brought an experienced head into the side, he is a great organiser and has good ability. He set up two goals at Wrexham showing great vision."
Latics will not comment until an official offer has been made, but he has been left in no doubt he is not in Paul Jewell's plans.
He has not played for the first team in more than a year.
Bristol City are the second side Dinning has been loaned out to this season, following a two-month stint at Championship rivals Ipswich Town, and the fifth club he has played for temporarily in his time at the JJB.
His Wigan contract expires at the end of this season and he is keen to sort out a
permanent deal in Bristol before his loan runs out after this weekend's home game with Sheffield Wednesday.
Dinning said: "From a personal perspective, I do not want to be going into the Wednesday game thinking it could be my last for City.
"I have made my intentions clear in that I want to come down for keeps and I am prepared to uproot the family and buy a house in the area. I am not going to be greedy over contracts and terms because I want to be fair to the club, who have been great to me.
"By the same token, I have to think of myself and my family at this stage of my career and ensure there is a decent enough deal to me through the next few years."
Meanwhile, midfielder Andreas Johansson is the latest name rumoured to be on Jewell's Christmas shopping list.
The Swedish international, who plays for Djurgarden in his homeland, could be a replacement for long-term injury victim Per Frandsen although Latics have stuck to protocol by not commenting on the speculation.