"He wants to play," Nets coach Steve Nash said of Harden prior to Game 5. "He has been pushing."
"I think it's James' decision" whether or not he plays, Nash added.
Harden participated in the Nets' shootaround Tuesday morning with improvement in his right hamstring, and that prompted the team to upgrade his status from doubtful to questionable for Game 5 in Brooklyn, New York, sources said.
The Nets are tied 2-2 in the Eastern Conference semifinal series with the Bucks and are preparing to be without guard Kyrie Irving (right ankle sprain) for the rest of the series, sources said. The team hasn't ruled Irving out beyond Game 5, but Harden is clearly much closer to a return.
Nash said Sunday that the team would try to approach the injuries as isolated incidents and not let Irving's ankle sprain rush Harden back to the floor before his hamstring is fully healed. Harden was injured in the first minute of Game 1 of the Nets' series against the Bucks on June 5.
Irving was injured midway through the second quarter of Sunday's Game 4 in Milwaukee when he landed awkwardly on Giannis Antetokounmpo's foot after making a layup over Jrue Holiday. Antetokounmpo crashed the paint in what was an attempt to help Holiday, who was the primary defender.
Irving remained on the floor for several minutes as Nash and the team's athletic trainers attended to him. Eventually, Irving walked to the locker room without assistance but was limping. He left the arena in a walking boot and on crutches. An MRI on Monday confirmed Irving's ankle sprain.
The Nets have battled injuries all season. The Big Three of Harden, Irving and Kevin Durant played just eight games together in the regular season and six games together in the playoffs -- including the game in which Harden was injured after just 43 seconds. Harden missed 18 games in the regular season with a hamstring strain, and before that he missed two with hamstring tightness.
ESPN's Malika Andrews contributed to this report.