Zinchenko, 29, has spent the last six months on loan at Nottingham Forest, but has only appeared in five Premier League games for the Tricky Trees.
According to several Dutch reports, including from De Telegraaf and Voetbal International, Ajax have nearly reached an agreement with Arsenal on a six-month loan deal for the Ukrainian international, with negotiations in the final stages.
Zinchenko's contract in North London is set to expire this summer, giving Ajax and Zinchenko the chance to freely explore a longer stay in Amsterdam.
Ajax have been in the market for new full-backs, with right-back Anton Gaaei and left-back Owen Wijndal allowed to leave the club this transfer window.
Former Arsenal defender Takehiro Tomiyasu joined the Amsterdam giants on a free-agent deal in December but hasn't yet played any minutes as he continues to build match fitness.
The experience Zinchenko would bring to a young Ajax core helps his case, too - Zinchenko, a 75-time Ukraine international, has played 150 Premier League games in his career and knows the Eredivisie well from his season-long loan at PSV during the 2016/17 season.
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