Odemwingie is a target for QPR who have already had a bid of £2million turned down by Albion during the current transfer window.
Garlick stressed that the Baggies have "no need" to sell any of their players.
Odemwingie has played a leading role in Albion establishing themselves in the Barclays Premier League and has been their top scorer for the past two seasons.
West Brom are keen to hold onto the services of a player who has 18 months remaining of a three- year contract.
Garlick said: "Peter is hugely popular with our supporters and it is disappointing that he has decided to hand in a transfer request.
"It was immediately turned down and has done nothing to change our stance during January. Peter is under contract until the summer of 2014 and we have no need or desire to sell our core players.
"We want to keep the squad intact to enable us to build on an encouraging first six months of the season."
Baggies head coach Steve Clarke has also delivered the same message on several occasions since the transfer window opened on January 1.
West Brom have also already rejected a £5million bid from QPR for central defender Jonas Olsson.