The Reds, who overcame Manchester City 5-1 on aggregate in the quarter-finals, will host Roma on 24 or 25 April before the return leg on 1 or 2 May.
Arsenal will face Atletico Madrid in the Europa League semi-finals, while Red Bull Salzburg meet Marseille.
The Gunners will play the first leg at home on Thursday, 26 April, with the second leg a week later on 3 May.
The Champions League final will be held in Kiev, Ukraine on Saturday, 26 May.
The Europa League final will be in Lyon, France on Wednesday, 16 May, with the winner guaranteed a place in next season’s Champions League.