The Reds went closest to breaking the deadlock via Roberto Firmino in the first half, but the Brazilian struck straight into the arms of David de Gea after the ball had deflected into his path.
United could have won it late on; however, Alisson Becker produced a fine block to keep out Paul Pogba’s close-range effort, ensuring the points were shared.
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Liverpool made one change from their last Premier League outing as Xherdan Shaqiri was handed a start in midfield. Joel Matip remained sidelined as he works his way back to full fitness, so Jordan Henderson began in defence.