The Seagulls midfielder, 24, has been in impressive form this season - and most-recently starred in the 1-1 draw with the reigning champions.
Alex Crook, talkSPORT's transfer guru, revealed the two Premier League giants' interest in Mali international Bissouma.
Crook told the Jim White Show: "Bissouma is a player (Mikel) Arteta is a big fan of.
“I know Arsenal are by no means the only big six club keeping tabs on him.
"He is looking for a replacement for the out of contract Gini Wijnaldum.
“Bissouma himself is contracted until 2023 so next summer would usually be the time when they would start negotiating a potential new deal."
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