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.
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.
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.
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.
Pep Guardiola isn't just losing on the pitch this season, but off it as well
