Bryant is recovering from a severely sprained left ankle as well as the flu.
"#countonthew #nomamba #noswan #noproblem. Great opportunity tonight," Bryant tweeted.
The Suns, blown out at Washington 127-105 two nights earlier, outscored the Lakers 28-10 in the fourth quarter to snap a four-game losing streak with their victory Monday night.
With Utah's loss to New York, the Lakers remain a game ahead of the Jazz for the eighth and final playoff spot in the West.
Bryant initially injured his ankle on the final play of a loss to the Hawks last week, landing on the foot of Atlanta's Dahntay Jones.
Bryant, the fifth-leading scorer in NBA history, spent two days trying to fight his way back, and played the first quarter in Indiana Friday night. But he sat out the remainder of Los Angeles' victory.
Los Angeles doesn't play again until Friday when it hosts the Washington Wizards, which could be long enough for Bryant to recover.
"Knowing Kobe, probably Friday, but that's day-to-day and we don't know that yet," coach Mike D'Antoni said when asked when Bryant might possibly return.
Sitting out until Friday would give Bryant a full seven day's rest since playing against Indiana before returning to the lineup.
"If we can win, it's a silver lining because he rests and gets his body in shape, but if we don't win, then it's not very good," D'Antoni said. "So it's a double-edged sword."
Information from ESPNLosAngeles.com's Dave McMenamin and The Associated Press was used in this report.