Thierry Henry has been heavily linked with a return to the Gunners in January whilst Cahill has indicated that he is keen on heading back to the Toffees for the winter.
But Roxburgh said that neither club has made contact with the Red Bulls about securing the loan services of the pair.
“Right now we don't have any requests for that. No one has requested for anyone to go on loan. If such a request came in, then we would have review each one,’’ said Roxburgh.
“It could be that something that can be helpful. The player has been injured and they need to come back in a competitive arena. It's possible.
“But it depends on the individual. It depends on the circumstances. You cannot say never on that one, but it's unlikely. It's unlikely at the moment that that would happen.”