The 17-year-old centre-back only joined the Gunners from West Ham United last year but Sky Sports News report that he is desperate for first-team football and already wants to move on.
Dallison has been training with the Seagulls over the past week, but his agent Alex Levick remained tight-lipped about the youngster's future.
"Tom is training with Brighton, that is all we can confirm at this stage," Dallison's agent Alex Levack told Sky Sports News.
"We can't comment on his future."
Aston Villa, Crystal Palace, Reading, Watford, Wolves and Sheffield United are also believed to be interested in Dallison.