But their NL East rivals, the Atlanta Braves, have also made a significant offer, sources indicated.
The Phillies continue to structure an offer around around their best pitching prospect, Jarred Cosart, and their best hitting prospect, first baseman Jonathan Singleton. They are currently playing for Class A Clearwater.
The Astros continue to push for two more high-end prospects, sources say.
The Braves' offer was said by one source to be built around highly regarded pitching prospects, but does not include much-coveted righthander Julio Teheran.
Multiple sources said interest in Pence heated up Thursday following the exit of Carlos Beltran from the trade market.
Six teams were known to have made contact with the Astros -- the Phillies, Braves, Reds, Red Sox, Pirates and Indians. The Astros continued to tell those clubs they would need to be overwhelmed to trade the 28-year-old Pence, but one source said they were "keeping an open mind" as they fielded offers.
One complication is that it's expected that any deal would have to be approved by outgoing owner Drayton McLane and Jim Crane, whose purchase of the club is expected to be finalized next month.
Jayson Stark is a senior baseball writer for ESPN.com.