New York Giants quarterback Mike Glennon. Danielle Parhizkaran/NorthJersey.com / USA TODAY NETWORK

The Miami Dolphins are down to their third-string quarterback, and they have added a veteran late in the season to address their depth concerns.

The Dolphins have signed Mike Glennon to their practice squad. Head coach Mike McDaniel told reporters on Wednesday that it is unclear if Teddy Bridgewater will be cleared to play in Miami’s season finale against the New York Jets.

Bridgewater suffered a dislocated finger on his throwing hand in last week’s loss to the New England Patriots.

Miami has already been without starting quarterback Tua Tagovailoa, who is dealing with another concussion. Reports have indicated Tagovailoa wants to play in the postseason if the Dolphins make it, but clearing concussion protocol may not be his only issue.

Glennon, 33, was a backup with the New York Giants last season. The journeyman started four games when Daniel Jones was injured and completed just 53.9 percent of his passes. Glennon threw for 790 yards with four touchdowns and a whopping 10 interceptions. He has 47 touchdowns compared to 35 interceptions in nine-plus NFL seasons.

The Dolphins still have a realistic shot at making the playoffs, though their quarterback situation is obviously a huge concern. They need to beat the Jets on Sunday and have the Patriots lose to the Buffalo Bills in order to clinch a spot.

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