The Daily Star Sunday says the Scotland international, 27, joined Palace from Wigan in a £7m deal last summer.
Alan Pardew has been impressed with him since he took over as boss and McArthur is in line for talks about a new contract. However, Palace may need to offload some of their squad to help make way for PSG midfielder Yohan Cabaye, 29.
Canaries boss Alex Neil played with McArthur at Hamilton.
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