Matviyenko was linked with Arsenal as a possible defensive signing this month as they look to bolster a weakened defence.
Now, with the injury to Shkodran Mustafi during the 2-1 win over Bournemouth on Monday night, the Gunners will be even more keen to sign reinforcements.
According to Ukrainian media outlet Komanda 1, Arsenal and Shakhtar Donetsk have thrashed out the 'nuances' of a deal in principle for Matviyenko.
The centre-back is a key man for Shakhtar and has featured 14 times in the Ukrainian Premier Liga this season.
Matviyenko also took to the pitch on both occasions when Shakhtar faced Manchester City in the Champions League group stage this season.
Arsenal boss Mikel Arteta would've had a close-up look at the player from the touchline, as he was Pep Guardiola's assistant at the time.
City were themselves thought to be interested in signing the Ukraine international, who featured on a list of reported defensive targets.
It was thought that Arsenal had already done a deal to sign Flamengo's Spanish centre-back Pablo Mari.
Mari was filmed arriving in London with Arsenal's technical director Edu Gaspar, for a medical.
However, he has since returned to Brazil and it is unclear whether the move is still on the cards.
26-year-old Mari offers slightly more experience in terms of age, but Matviyenko, 23, has more top-level experience in Europe.
Arsenal's pursuit of both players now appears to be or have been close to completion - time will tell which defender they opt for, if either.
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