Gillespie suffered a right ankle fracture and will be re-evaluated in four weeks, Shane Young of Forbes.com reports.
Gillespie rolled his ankle during Friday's 133-118 loss to the Santa Cruz Warriors, Gerald Bourguet of GoPHNX.com reports.
Gillespie signed a two-way deal with the Suns on Monday, Adrian Wojnarowski of ESPN reports.
The Nuggets are declining to extend Gillespie (knee) a $1.87 million qualifying offer prior to Saturday's deadline, making him an unrestricted free agent, Vinny Benedetto of The Denver Gazette reports.
Gillespie (knee) is inactive Sunday versus Memphis.
Gillespie is doubtful for Sunday's game against the Grizzlies due to a left knee sprain.
Gillespie is probable for Sunday's game against the Trail Blazers due to a right ankle sprain.
Gillespie finished with six points (3-7 FG, 0-2 3Pt), one rebound, three assists and two steals in 20 minutes during Sunday's 107-104 loss to the Rockets.
Gillespie racked up five points (2-4 FG, 1-3 3Pt), one rebound and two assists over 12 minutes during Saturday's 123-101 win over Chicago.
Gillespie produced 13 points (4-11 FG, 2-7 3Pt, 3-3 FT), four assists, three rebounds, one steal and one block in 22 minutes during Thursday's 133-124 double-overtime loss to the Bulls.