The 26 year-old has spent the last three months at Blundell Park, scoring nine goals in fourteen matches for the Mariners in the process.
In the final game of his loan period, Hannah scored the winner in Grimsby's 1-0 win over Wrexham this Friday to send them top of the Blue Square Bet Premier.
Hannah's impressive form during his time with the Mariners is believed to have put the forward on the radar of a number of Conference clubs.
Grimsby themselves are keen to try and bring the forward back to Blundell Park, but Parkinson has stressed that any new move away from Valley Parade for Hannah must now be a permanent one.
"Ross Hannah was back with us as of yesterday (Sunday) morning," Parkinson confirmed.
"He did really well during his time at Grimsby and we were all pleased to see him get some goals under his belt.
"There were times when we could have called Ross back given the amount of games we've had in periods this season, but we decided to be fair to Ross and to Grimsby.
"We wanted to give Ross the full three months at Grimsby.
"As you may expect given the amount of goals he's scored, there has been some interest in Ross from other clubs.
"We have stressed to Grimsby and to any other club interested in Ross that he is not going anywhere else on loan.
"If any of the interested clubs make an offer for Ross that we feel is right for the club and for Ross, we'll listen to it.
"Until then though, we look forward to working with him once again."
At the same time as Hannah comes back into the club, first year pro Adam Baker has joined Blue Square Bet North side Harrogate Town on a month's loan.
Parkinson added: "It will be a good chance for him to enjoy a solid month of playing football and getting some games."
"It will be a good test for him. Harrogate is a good club and they play good football."