The 22-year-old midfielder has a deal on the table and has until June 17 to decide whether to accept the terms.
But even if he turns down the offer, there is no certainty that the player will be leaving Carrow Road.
Doncaster told the club's official website: "In March, Darel was offered a two-year contract extension and a further two-year option - this was not accepted.
"The club therefore offered a one-year extension to protect its compensation rights under Football League regulations, as Darel is still under 24.
"He has until June 17 to accept or decline that offer. If he accepts, that's fine of course, but if he declines or fails to respond, we have the ability to put him on a week-to-week contract to protect our rights to compensation should another club come in for him."
Russell missed part of last season after having surgery on an injured ankle but featured regularly towards the end of the campaign as The Canaries just missed out on the play-offs.
