The Knicks made the Argentine point guard a qualifying offer of $988,872 last month, making him a restricted free agent.
"I would like to go back to New York," he told ESPNNewYork.com. "I miss New York."
New York has its mini mid-level exception of $3.1 million, which it could opt to split between Prigioni and fellow free agent Chris Copeland, who has reportedly drawn interest from a number of teams.
With the retirement of Jason Kidd, the Knicks currently have only one point guard on the roster in Raymond Felton.
The Knicks went 16-2 down the regular season stretch with Prigioni in the starting lineup.
Chris Smith, the younger brother of Knicks' free agent guard J.R. Smith, previously told SNY.tv he was hoping to land a gig as the Knicks backup point guard.