Arsenal turned to the experienced stopper to provide backup to Bernd Leno, deeming last summer’s signing Alex Runarsson not ready for Premier League football.
Football.London says Arsenal are expected to turn the loan into a permanent deal in the summer.
There was no option to buy when a loan was struck in January, so Arsenal and Brighton would have to agree a fee for the goalkeeper.
Ryan was a constant in the Brighton side following their promotion to the Premier League in 2017.
He has made 123 appearances for the Seagulls since joining from Spanish side Valencia.