Garcia was one of Heart's best players in the 2012/13 A-League season, scoring six goals and setting up four more in his 24 matches, before being named the club's Player of the Year at the end of the campaign.
But having signed with Heart before last season due to a lack of other options, Garcia is using his good form to secure a better deal somewhere else, although the Red and Whites' CEO Scott Munn remains confident of keeping the midfielder in Melbourne.
"We'd love to have him for another season," Munn told Melbourne radio station SEN. "We were lucky enough to get Richie last year, late.
"He wasn't able to secure a deal (elsewhere) and we've put forward what we think is a really competitive offer.
"He's still having a look around what's in the marketplace and we're confident but until there's a piece of ink on a piece of's not a done deal."
After missing out on the A-League finals last season, Munn says Heart are looking to invest more money in their football department in an effort to improve their results on the pitch.
Munn, who has been critical in the past of marquee players, claimed Heart were interested in bringing a high-profile player to the club if he could perform on the pitch, while the CEO added the Red and Whites will give head coach John Aloisi more support in the coming season.
"We're probably going to add a few more staff around him this year and I think that's one of the most important things after last year," Munn said.
"Our board was really clear in investing more money into the football department.
"We didn't do that last year and we'll see more players, a higher spend on salaries and also in the football department."
Aloisi has already begun pre-season training with his squad and expects Harry Kewell and Dutch defender Rob Wielaert to arrive in Melbourne next week but Munn has made it clear recruitment is not finished with two 'big signings' still to come.
Heart are also looking forward to having young winger Mate Dugandzic, who missed most of last season with a foot injury, back involved next season and the 23-year-old believes his rehabilitation is tracking well.
"It's coming along really well now," Dugandzic told Heart's website. "I've started training with the guys now (and) last week was my first session.
"I think it's been about eight months since the injury so I am very happy with how things are progressing.
"I've been training with the boys three or four times a week, not fully yet, but it's getting there definitely."