ESPN is reporting that both of the London clubs are keeping an eye on the 27-year-old shot-stopper with a view to a possible transfer move for him.
The RB Leipzig goalkeeper spent five years playing at Liverpool but failed to make the grade at Anfield – and he is now attracting interest from some top clubs.
The same report claims that both Arsenal and Chelsea sent scouts to watch Gulacsi in action for Leipzig in the 2-0 defeat by Bayern Munich on Saturday.
Arsenal are thought to be on the lookout for a long-term successor to Petr Cech, who is 35 and has 18 months left on his current contract at The Emirates.
Chelsea, meanwhile, are apparently worried that they could lose their first-choice shot-stopper Thibaut Courtois to Real Madrid.
Gulacsi failed to make a single first-team appearance for Liverpool during his time at the Merseyside outfit.
However, he is now regarded as one of the top goalkeepers in Germany, and it remains to be seen whether Arsenal or Chelsea will make official bids for the shot-stopper as the January transfer window looms large.
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