The Portuguese coach's exit followed growing tensions with senior Old Trafford officials, including director of football Jason Wilcox, over recent days.
Following on from a run of nine defeats in 12 games in all competitions, Liverpool are unbeaten in their last nine, although that sequence includes four draws.
Former world number one Daniil Medvedev extended his impressive start to the season ahead of the Australian Open with a straight-sets win over Frances Tiafoe in Brisbane on Wednesday.
The fourth edition of the Women's Premier League launches on Friday with the popularity of women's cricket at an all-time high in India following their maiden World Cup triumph.