Wolves left-back Ait-Nouri is expected to complete a £34 million move to the Etihad Stadium over the weekend, Sky Sports reported.
An initial £46 million deal for Dutch midfielder Reijnders has been agreed with AC Milan, along with add-ons potentially taking the transfer to £59 million.
City chairman Khaldoon Al Mubarak promised last week to conduct "swift" transfer business in order to give Pep Guardiola's men the best chance of winning the Club World Cup.
Lyon playmaker Rayan Cherki could also be signed in time for the tournament in the United States as negotiations between City and the French club are ongoing.
City will face Moroccan side Wydad AC and Emirati club Al Ain before a clash of European heavyweights with Juventus in the group stage, which kicks off on June 14.
After missing out on a major trophy in the recently completed season for the first time since 2016/17, City are hoping to bounce back quickly with a major overhaul of Guardiola's squad.
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They also spent more than £172 million in January on Omar Marmoush, Abdukodir Khusanov, Vitor Reis and Nico Gonzalez.
The raft of new arrivals, however, could spell the end of England winger Jack Grealish's City career.
Grealish, who remains City's record signing after a £100 million move from Aston Villa in 2021, will reportedly be left out of Guardiola's 35-man squad for the Club World Cup.