Baggies boss Steve Clarke was assistant manager to Kenny Dalgish as the Reds lifted the cup in Wembley in February with victory over Cardiff.
The Red Devils also face top-flight opposition in their bid for silverware, with Alan Pardew's Magpies set to visit Old Trafford - the first game out of the hat in Thursday night's draw.
Manchester City host Aston Villa while Coventry are faced with a daunting trip to the Emirates Stadium to take on 2011 runners-up Arsenal.
European champions Chelsea host recently-relegated opposition in the form of Wolves, who were the last side to book their place in the third round with victory over Northampton tonight.
Andre Villas-Boas' Tottenham make the long trip to Brunton Park and Carlisle, while Everton cross the Pennines to take on Leeds.
QPR and Reading face off at Loftus Road and West Ham welcome Wigan in the two remaining all Premier League encounters.
Martin O'Neill's Sunderland head to MK Dons with Southampton hosting their former manager Dave Jones as he returns to St Mary's with new club Sheffield Wednesday.
Norwich are at home to Doncaster while Swansea travel to Crawley, and Swindon's reward for ousting Stoke is a home tie against Burnley.
Middlesbrough venture to Deepdale to face Preston with Bradford taking on Burton in the only match involving two League Two clubs.
Capital One Cup third round draw:
Man Utd v Newcastle, Man City v Aston Villa, MK Dons v Sunderland, West Brom v Liverpool, Crawley v Swansea, QPR v Reading, Norwich v Doncaster, Bradford v Burton, Preston v Middlesbrough, Arsenal v Coventry, Southampton v Sheff Wed, Chelsea v Wolves, Carlisle v Tottenham, Swindon v Burnley, West Ham v Wigan, Leeds v Everton.
Ties to be played week commencing September 24