NASHVILLE, Tenn. — Patience appears to be paying off this time for Mariners general manager Jack Zduriencik as he wrapped up the baseball winter meetings with some big targets in his sights.

The biggest is free-agent outfielder Josh Hamilton, whom the Mariners are said to be “very close” to reaching a deal with due to an ever-shrinking market for his services.

The list of potential suitors for Hamilton grows smaller by the day, with his former Texas Rangers club apparently being the most serious competitor standing between the Mariners and having the slugging outfielder come to Seattle.

The Rangers are waiting to see whether they can sign free-agent pitcher Zack Greinke to a contract in the $150 million range and were also reported by be trying to land outfielder Justin Upton from the Diamondbacks in a multi-team trade.

Either move would likely price the Rangers out of the Hamilton market and leave the door wide open for Zduriencik, who left the meetings Thursday morning in somewhat of a holding pattern on big-ticket acquisitions.

“A lot of things are out of your control, there’s no doubt,” Zduriencik said, without referring to any targeted player by name. “

A source said the Mariners and Hamilton were “very close” to a deal depending on what happens next with Greinke. A report by FOX said the two sides had already discussed multiple three-year offers in the $20 million to $25 million-per-season range.

Mariners president Chuck Armstrong did not deny the Mariners were still pursuing Hamilton.

“We’re still interested in him, yes,” Armstrong said.