The Magpies and Rovers drew 1-1 at St. James' Park on Saturday, meaning there will be a replay at Ewood Park on a day to be confirmed next week.
And the winners will have a home tie against Watford later this month. Fourth round ties will take place between 25th and 28th January.
The fourth round draw was made on Monday evening by former Wolves goalkeeper Carl Ikeme and ex-Liverpool frontman Robbie Keane.
Newcastle have already faced the Hornets twice this season in the Premier League, winning 1-0 at St. James' Park in November before drawing 1-1 at Vicarage Road in their final game of 2018.
And United met Watford on their way to winning the competition in both 1924 and 1932.