Hamilton said he hadn't spoken to Moye to find out the details, but said it was supposed to be a "feeling out" session. Hamilton said he ran into co-chairman of the board Ray Davis on Wednesday.
"He said he'd met him and was really impressed by him," Hamilton said. "He's not a prototypical agent and that impressed him."
Hamilton said he was a little surprised the two sides met but is pleased that they are talking.
"It's not going to happen any time soon," Hamilton said, "but I'm glad communication is open."
As the offseason began -- and before he had a relapse with alcohol in late January -- Hamilton had set a deadline for the start of spring training to get a deal done. Both sides decided to table talks after Hamilton's relapse to give him time to focus on his recovery and family.
Hamilton said he doesn't have any problems with his agent and the club talking and that he's going to get updates only when his agent feels it's necessary.
"It's good that I don't know all the details," Hamilton said. "It keeps me from being weird around front office people, too, if I really don't know what's going on until it gets very serious. I don't think it's at that point. I think they want to get an idea, each side, and feel things out. We've expressed what we'd like to do contract-wise."
Hamilton said he wants to stay in Texas and hopes the sides can come to an agreement at some point, though he concedes negotiations take time.
"I would like to stay here," Hamilton said. "Just like every other important decision, we pray about it and try to figure out God's will. This is a good place. I enjoy it. I enjoy the area. The Metroplex is a good place to raise a family."
Hamilton, the 2010 American League MVP, is making $13.75 million this season as part of a two-year deal he signed before last year that got him through his arbitration years.
The Rangers typically don't negotiate during the season, but general manager Jon Daniels has said that he's willing to do it if talks stay private and it doesn't distract the player or the team. The Rangers just completed a five-year, $75 million deal with second baseman Ian Kinsler with a $10 million option for a sixth year earlier this week.