Russell signed on at St James Park until the end of the season with a view to a permanent move and, having returned to action after a knee injury curtailed his solid start, he is looking to continue where he left off and earn a full-time switch.
"As far as I'm concerned I'd like to come down, but it's a case of sorting things out between the two clubs," he told the Gloucestershire Echo. "Obviously I've still got a year left at Cheltenham so I'll have to wait and see.
"Apart from the injury I've loved my time at Exeter and enjoyed being part of the squad."
The Grecians are currently battling it out for automatic promotion from League Two while Cheltenham continue to live for another day at the wrong end of League One after Northampton drew 3-3 with Scunthorpe on Tuesday night.