"Me, Horc (Shawn Horcoff, of the Edmonton Oilers), Howie (Jimmy Howard), Kroner (Niklas Kronwall) and maybe (Jonathan) Ericsson and Monster (Jonas Gustavsson) are going," Cleary told the paper.
"Our goal is to get a good week of five-on-five games, with maybe a referee, focusing on the little things: stopping and starting, the attention to detail, the defensive side of the game, a little bit. And, if things go well, it'll make sure you're ready."
A large number of NHL players have practiced in the desert since the start of the lockout. Pittsburgh Penguins captain Sidney Crosby led the charge, with the likes of San Jose's Patrick Marleau, Buffalo's Ryan Miller, New Jersey's David Clarkson and Dallas' Brenden Morrow also recruiting others to join them.
The News suggests as many as 30 players will be in Arizona by the time Cleary and Co. arrive, creating some solid workouts for those hoping for the NHL and NHLPA to come to terms on a new CBA before next Saturday.
"I think it's going to be good," Howard told the paper. "It's going to be scrimmaging scenarios and they said a possibility during the scrimmages was having refs out there. So I think that's very beneficial for us, as goalies, especially for myself, just getting down there and having full-on practices and the scrimmages, possibly having some more game-like situations."
The NHL and NHLPA have until the end of Jan. 11 to reach an agreement, or else the League will cancel the entire season.
The two sides have made significant progress over the last week, but around seven main issues remain unsettled.
Roughly 13 hours worth of separate mediation sessions took place on Friday, and that process will resume this morning.
If a deal is ironed out in the coming days, Cleary welcomes the short trip to Phoenix.
"We'll just jump on a plane and come back," he said. "There's nothing to it."