Jurgen Klopp’s men head into the game looking to build on their dramatic 2-1 win over Crystal Palace at Selhurst Park in the Premier League last weekend.
United, meanwhile, are looking to bounce back after they slumped to a 1-0 loss to West Bromwich Albion at The Hawthorns on Sunday.
It is the first time that Liverpool and United are locking horns in European competition.
And former Liverpool boss Rodgers, who was replaced by Klopp at Anfield back in October, is expecting to see a cagey affair on Merseyside on Thursday night.
Speaking to the Belfast Telegraph, Rodgers said: “I was always pleased to be involved in those games as the manager of Liverpool.
“It will be tight but Liverpool are coming off the back of good results so they will go into Thursday’s first leg with confidence.”
“United will feel, having done the double over Liverpool, that they also have a good chance. It will be tight.”
United have won their last four Premier League fixtures against Liverpool since a humiliating 3-0 home defeat in March 2014.
Liverpool are unbeaten in eight European games this season, and have not lost in six Uefa home matches.
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