The imposing 17-year-old centre-half was snapped up by Arsenal from West Ham United last summer - but he looks set to move on before his current deal expires at the end of the season.
Dallison is keen to push on play first-team football as soon as possible, and a host of clubs are battling for his signature.
Arsenal have allowed him to train with Brighton this week, and they are keen on securing a deal.
However, the likes of Aston Villa, Crystal Palace, Reading, Watford, Wolves and Sheffield United are all reported to have an expressed an interest in talking to Dallison before he commits his future anywhere.
Dallison's agent Alex Levack of SideKick management told Sky Sports: "Tom is training with Brighton, that is all we can confirm at this stage - we can't comment on his future."