Blount suffered the injury in Sunday's game against the Houston Texans, becoming New England's latest prominent player to go down with a season-ending injury.
Blount, 29, has rushed for a team-leading 703 yards and six touchdowns this season. He was a key contributor in New England's Super Bowl run last season, including his stellar performance in the AFC Championship Game in which he ran for 148 yards and three touchdowns.
The Patriots met Monday with former NFL RB Steven Jackson in an effort to bolster their running back corps, a source told ESPN's Ed Werder.
The meeting was just preliminary, but there is mutual interest, the source said.
Jackson played for Patriots offensive coordinator Josh McDaniel during his time with the St. Louis Rams, though he hasn't worked out for any team this season.
Blount's injury prompted the Patriots to sign third-year player Montee Ball, a 2013 second-round draft choice of the Denver Broncos, to the practice squad Tuesday.
New England also has undrafted rookie running back Trey Williams on the practice squad. The Patriots worked out rookie Alonzo Harris, who made the Green Bay Packers' roster as an undrafted free agent and was cut earlier this month, on Tuesday.
Bolden entered the NFL with the Patriots as an undrafted free agent in 2012 and primarily has made his mark on special teams. He took over for Blount on Sunday night and finished with 16 carries for 51 yards.
Bolden, who is 5-foot-11, 220 pounds, has 174 carries for 744 yards and six touchdowns in his NFL career.
White, at 5-foot-10 and 205 pounds, is more of a "passing back." He has 16 carries for 41 yards and two touchdowns in 11 games this season, to go along with 26 catches for 248 yards and two touchdowns.
The Patriots (11-2), who have the best record in the AFC and clinched a postseason berth Sunday, already are without starting left tackle Nate Solder and running back Dion Lewis for the remainder of the season. New England also has played its past four games without star receiver Julian Edelman, who is out indefinitely with a broken foot.
ESPN Patriots reporter Mike Reiss contributed to this report.