Adrian Wojnarowski of The Vertical reported Rubio "remains a significant target" for New York as it looks to bolster its backcourt in the final hours before the trade window closes.
Marc Stein of ESPN reported the Knicks are hoping to land an additional asset from Minnesota in a potential deal featuring Rubio and Derrick Rose. That's the main reason negotiations have continued right up until deadline day.
Meanwhile, sources around the league believe president Phil Jackson is a "fan" of the T-Wolves point guard, per Ian Begley of ESPN.
Sam Amick of USA Today noted other teams are involved in talks with Minnesota, too:
Rubio told Jerry Zgoda of Star Tribune in late January he was trying to ignore the trade rumors in the final weeks leading up to the deadline.
"Just do what I do," he said. "My name or every name is going to be out there at some point, but you can only worry about things you can control. Right now, what I can control is playing my best and do what I've been doing."
The 26-year-old Spanish playmaker is a terrific distributor (8.4 assists per game), rebounds well for a guard (3.8 boards) and is active in passing lanes defensively (1.8 steals).
He's never developed consistency with his shot, however. The 2009 fifth overall selection holds a 37.1 career shooting percentage, including a 31.1 mark from beyond the arc. That's prevented him from becoming a top-tier asset at the position.
Rubio is under contract through the 2018-19 campaign with a cap hit that steadily rises to $14.95 million in the final season, according to Spotrac. On the flip side, Rose will become a free agent at season's end. So New York could let him walk, clear cap space and start fresh at the position.
It's unclear exactly what the Knicks want the Timberwolves to add in order to complete the trade.