The Astros announced Oct. 31 they had declined to exercise their 2007 option on Bagwell's contract, seemingly ending a 15-year relationship with the ailing star.
Bagwell officially filed his paperwork Saturday, but Axelrod says he would like to remain with Houston in some capacity.
"This is entirely a procedural matter," Axelrod said. "Today is the last day for free agents to file, and even players contemplating retirement complete the filing process. This is completely a technical matter and does not change anything about the relationship between Jeff and the Astros.
"Our hope is that some time in the near future, we will arrive at a long-term arrangement that will keep Jeff as a part of the Astros' family for many years."
The franchise's all-time leader in home runs, Bagwell received a $7 million buyout of the option. The 38-year-old received $17 million in 2006 despite missing the entire campaign with an arthritic right shoulder.
Bagwell is the only first baseman and one of only 10 players all-time to hit 400 home runs and steal 200 bases. In 15 seasons -- all with the Astros -- the four-time All-Star and 1994 National League MVP hit .297 with 449 home runs, 1,529 RBI and 202 steals in 2,150 games.