Albion have been drawn away to non-League Lincoln or Ipswich in the fourth round of the FA Cup.
They will discover their opponents on January 17, when Lincoln stage their replay with Ipswich at Sincil Bank.
The National League leaders led twice at Portman Road on Saturday but were eventually held to a 2-2 draw by one of the Seagulls' Championship rivals.
Albion dew 0-0 at Mick McCarthy's Ipswich in the league in September.
They were beaten 3-1 in the first round of the FA Cup on their last visit to Lincoln in November 2003.
The fourth round tie, which takes place between January 27 and 30, means Albion face three away games in a row.
It is followed by the trip to Huddersfield on Thursday February 2 and Brentford on Sunday February 5.
The Seagulls could have another Saturday league game postponed as a result of the fourth round draw.
They are due to visit Barnsley on the fifth round date, February 18. Barnsley are away to Blackburn if they win their replay at home to Blackpool.
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