Mullin's future will now be part of a wider transfer discussion between Parkinson and the club's owners at Wrexham. The club currently sit in ninth place in the Championship, with Parkinson telling reporters after the FA Cup win over Nottingham Forest that the club could look to improve the squad.
"We'll have a chat next week as a group. We've got players coming back into the group [from injury], but if we do make any signings hopefully they'll be strategic ones and give the group a lift," he said. "We don't want to make signings for the sake of it. But if we can make improvement and feel it's the right decisions, then we'll go for that."