The 30-year old USA forward made a surprise big-money move from Tottenham to Seattle Sounders last weekend with some reports suggesting he had also been approached by the Red Bulls.
But Roxburgh, although admitting he was aware of Dempsey's availability, said that New York never made an official pursuit for the former Fulham star.
"We were just made aware that he was about to move," Roxburgh said.
"So we were made aware of that, and he obviously made a move and went to Seattle. He's a good player I hope it goes well for them and him. It's not a matter of us (rejecting him). We didn't pursue anything here.
"It's not a matter of becoming engaged in that discussion about that. We were just made aware that he could come to the US. That was really all. And before we knew it, he went to Seattle."