But there is still no place for star overseas signing Mohammad Nabi.
Cobb suffered a hamstring injury while batting in the defeat to Notts Outlaws on Sunday and needed Ricardo Vasconcelos to return to the wicket and be his runner.
It was hoped that the injury wasn't too serious to Cobb and he has been named in the squad to take on the Bears, but an extra batsman has been added to the 13 named for Sunday's fixture, with Ben Curran getting the call.
Nabi remains unavailable as he completes his mandatory Covid-19 quarantine in a London hotel, having arrived in the UK on June 5.
The Afghanistan all-rounder is expected to be part of the squad that will travel to Derby for the next Blast encounter against the Falcons on Thursday night.
The Steelbacks are still looking for their first win of the season having lost at home to both Worcestershire Rapids and the Outlaws.
By contrast, the Bears arrive in Northampton having won two and lost one of their three matches to date, which have all been on the road due to England playing New Zealand at Edgbaston in the second Test.
England all-rounder and World Cup winner Chris Woakes is in the squad for the date at Wantage Road, as is West Indian big-hitter Carlos Brathwaite, the man who smashed Ben Stokes for four successive sixes in the final over to win the World T20 Final back in 2016.
The Bears will be without the injured Adam Hose and Henry Brookes, while Rob Yates is still ruled out by illness and former Northants pace ace Olly Stone is unavailable as he is still part of the England group.
The match is an 1,100 sell-out and starts at 6.30pm.
Steelbacks squad: Josh Cobb, Ben Curran, Nathan Buck, Brandon Glover, Rob Keogh, Richard Levi, Wayne Parnell, Adam Rossington, Ben Sanderson, Tom Taylor, Charlie Thurston, Ricardo Vasconcelos, Graeme White, Saif Zaib
Bears squad: Will Rhodes, Carlos Brathwaite, Tim Bresnan, Danny Briggs, Ethan Brookes, Michael Burgess, Sam Hain, Olly Hannon-Dalby, Jake Lintott, Pieter Malan, Craig Miles, Dan Mousley, Ed Pollock, Chris Woakes