Marquez, who has spent the past seven years with Barcelona, has been strongly linked with the Red Bulls, who recently brought in former Arsenal striker Thierry Henry after he was freed from his contract with Barca.
"We hope to be able to have good news with Rafa, sometime in the near future, hopefully we will be able to present him to the public," Garber told reporters at half-time in the game between MLS All Stars and Manchester United on Wednesday.
"There is no news yet, but if we can bring in Marquez, the captain of the Mexican national team, a guy who had a great World Cup, a long time Barcelona player, if we could have him in MLS, it would really give us a big boost of credibility and I think would be exciting for our fans," Garber said.
Marquez, who can operate as a centre-half or a defensive midfielder, would be the Red Bulls' third 'designated player', whose wages are mostly outside of the salary cap, along with Henry and Colombian Juan Pablo Angel.
The league's highest profile designated player is LA Galaxy's English midfielder David Beckham while Mexican international Nery Castillo recently signed up with Chicago Fire.
ATTRACTING TALENT
Garber said that a league board meeting on Wednesday had discussed ways in which MLS could bring in more foreign talent to the competition.
"We spent a little time talking about what we need to do to bring more star players into the league now that we have Thierry Henry and Juan Pablo Angel and we are going to try and find ways that we can bring more of those kinds of players into Major League Soccer," he said.
Garber said in an interview with Sports Illustrated's website on Wednesday that some MLS teams had contacted Real Madrid's Raul before his move to Schalke and also responded to suggestions LA Galaxy were trying to sign Brazilian Ronaldinho from AC Milan.
"I don't believe that's something that's going to happen this year. That being said, the fact that our owners are interested in bringing a player like Ronaldinho to the league speaks to a bit more aggressiveness as it relates to player signings.
"I think that's good for our fans, and I think it's a good approach to try to capture some of the interest of those 24 million people (in America) who watched the World Cup final," he said.
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