He was absent from the session the day before their Champions League opener at home to Villarreal.
Tottenham visit Albion in the Premier League on Saturday.
Solanke has not featured for Spurs since the 2-0 victory at Manchester City on August 23 due to a troublesome ankle issue.
The injury sidelined the striker for much of pre-season and, despite being fit enough to play in Tottenham’s first three competitive fixtures under new boss Thomas Frank, he has since been consigned to the treatment table and was a notable absentee at the club’s open training session on Monday.
Centre-back Radu Dragusin, who was not played since he sustained anterior cruciate ligament damage in January, was involved in the non-contact element of the session before he trained individually.
That would appear to suggest he, at best, faces a race against time if he is to face the Seagulls.
Late summer signings Xavi Simons and Randal Kolo Muani both featured in wet conditions in Enfield, with Kolo Muani in line to make his Spurs debut on Tuesday night.
Spurs enjoyed a 3-0 win at West Ham on Saturday as they bounced back from the shock 1-0 defeat at home to Bournemouth.