Both are hampered by injuries last season and have spent the offseason rehabilitating, though both are expected to be ready for the start of preseason training next week. Robinson, 31, needed most of the season to recover from knee surgery and returned to action in September, but played only 30 minutes in one league match.
Mulrooney, 33, played in 14 games before suffering a knee injury that sidelined him for the rest of the season. He won the 2006 MLS Comeback Player of the Year Award after recovering from a torn ACL.
Both were members of San Jose's 2003 championship teams and the back-to-back champions fielded by the Dynamo in 2006 and 2007. Robinson also played one game as a rookie in the Quakes' 2001 championship season.
Coach Dominic Kinnear needs as many healthy veterans as he can field. Dwayne De Rosario moved north to Toronto after the 2008 season, and Seattle claimed Nate Jaqua in the expansion draft that year. From the 2009 squad Ricardo Clark (Eintracht Frankfurt) and Stuart Holden (Bolton) have headed overseas, though Houston retains the MLS rights to both players.
Houston is one of four MLS teams that will play a knockout tournament in Florida next month. Houston plays New York and Dallas faces Toronto on Feb. 25, with a third-place game and championship match following two days later at the ESPN Wide World of Sports Complex in Lake Buena Vista, Fla.