Finley is recovering from neck fusion surgery and is not yet medically cleared.
The Packers selected TE Richard Rodgers in the third round of the NFL Draft.
"I don't necessarily think the two are tied at all," Thompson said. "We were just trying to pick a good player."
Finley played under new Giants Offensive Coordinator Ben McAdoo, who was the tight ends coach for six seasons in Green Bay.
New York Giants