Newly-promoted Al-Mesaimeer has negotiated with the Iranian iconic midfielder to sign him.
Contract negotiations are underway between Al-Mesaimeer and Nouri, according to Qatari media.
Nouri has already said he would rather stay in Persepolis.
He helped Persepolis to reach Round of 16 of the AFC Champions League.
Persepolis finished in eight place last year in the Iranian Professional League (IPL).