NZonzi is currently in Russia with France as Les Blues prepare for a World Cup semi-final showdown with Belgium on Tuesday night.
Transfer talks between NZonzi and his suitors are on hold, as the midfielder focuses all his efforts on helping France progress to the final.
NZonzi has long been linked with a switch to Arsenal, but Le 10 Sport claim two new contenders for his signature have emerged.
West Ham and Everton want to sign NZonzi and both clubs are credited with a serious interest in the former Stoke star.
NZonzi is keen to exit Sevilla after a difficult last 12 months at the club that saw him fall out with the manager.
Arsenal have been tracking NZonzi at Sevilla and watched from afar as the 29-year-old blossomed into a formidable force in La Liga.
Sevilla are thought to be open to allowing NZonzi to leave, although there has been no official offer from Arsenal or their rivals.
NZonzi will remain focused on his international duties, but a bidding war could erupt once the tournament in Russia is over.
Arsenal have already made three major signings this summer and are poised to seal two more this week.
Midfielders Matteo Guendouzi and Lucas Torreira are scheduled to undergo medicals on Monday and could be confirmed as Arsenal players by the end of the day.
The duo would join Bernd Leno, Stephan Lichtsteiner and Sokratis Papastathopoulos as Unai Emerys first signings in his Arsenal tenure.