Francisco, 30, is a free agent at the end of the season.
"I would love to stay here because this group of guys is outstanding," Francisco said. "Everybody here wants to win and works hard for that. We deserve to win. We want it bad. I want to be a part of the winning here."
Francisco is 11-11 with a 3.75 ERA and 30 saves in 43 opportunities in five big league seasons with Texas. Francisco, who was acquired by the Rangers in 2003 as part of a deal that sent Carl Everett to the White Sox, made his Major League debut with the Rangers in '04.
The Rangers said it's premature to discuss Francisco's contract situation.
"It's something we are going to evaluate as the season progresses," Rangers assistant general manager Thad Levine said. "I think we have a very good relationship with Frankie and his agent, and if there is an opportunity for a discussion, I think both parties would be open to it, so we are going to see how it plays out."
Francisco converted 25 of 29 save chances last season and struck out 57 batters in 49 1/3 innings. Opponents hit only .214 against him, but he also battled the injury bug. The closer missed 44 games because of three stints to the disabled list for right biceps tendinitis (May 7-21), right shoulder tendinitis (June 4-19) and pneumonia (July 11-Aug. 1).
In the event of an injury to Francisco, the Rangers are covered. Darren Oliver and Neftali Feliz can take over the ninth-inning job. The organization also has pitching prospects Alexi Ogando, Tanner Scheppers and Pedro Strop in the Minor Leagues.