Muliaina, the All Blacks incumbent full-back, was switched to centre during the Chiefs Super 14 win over the Reds at the weekend when Sam Tuitupou was injured.
However, having moved to the Chiefs from the Blues this season, Muliaina would prefer to concentrate his efforts on the number 15 jersey, though he admits playing in the centre could be in his long-term plans.
But Latham believes the All Blacks selectors should resist the urge to switch him to centre.
"I don't see why you would want to move one of your best players from his best position," he told The Sunday Star Times.
"He's a talented and gifted player and has to the ability to shift but he's one of the best full-backs going around.
"I know it took me a while to get where I am so I tend not to want to swap positions. I would not mind betting Mils feels the same and is a bit sick of all the attention."
Muliaina has played at centre before. In last year's All Blacks trial coach Graham Henry was keen to see him in the number 13 shirt and selected him alongside Umaga in the Probables versus Possibles game.
The 25-year-old has also played there for Auckland in the NPC and for the Blues in the Super 12.
With Umaga retired and Smith suffering a broken leg, Henry has a few possible options available to him apart from Muliaina.
Ma'a Nonu has been playing well at centre for the Hurricanes and could be paired alongside stalwart Aaron Mauger without causing too much disruption to the All Blacks back line.
Anthony Tuitavake, of the Blues, has also been mentioned as has Crusaders wing Rico Gear, who has also played centre for the Blues.