The Premier League leaders have already seen two offers for the Shakhtar Donetsk winger rejected but remain in talks with the Ukrainian club.
Arsenal’s most recent offer is thought to have been worth around £60m, falling some way short of Mudryk’s valuation.
While Shakhtar are believed to be looking for a fee of around £85m, there is a hope a compromise can be reached, particularly with the 22-year-old expressing a desire to move to the Emirates Stadium.
Mudryk, who remains Mikel Arteta’s top target, has travelled to Turkey on Shakhtar’s mid-season training camp following the winter break in the Ukrainian top-flight.
Still, speaking to Lord Ping, Sagna predicted Arsenal would get their man but hinted a deal could have to wait until the end of the window.
“He’ll be joining the club,” he said.
“I think football transfers are a mind game between the buyer and the seller. Shakhtar knows the quality of the player and they know that Arsenal really want him.
“I think it will happen, but maybe at the end of the window.
“Shakhtar will keep pushing and negotiating until the end to get the largest amount for their player, but they will be aware of the players desire to join the club and they won’t want to frustrate the player.
“It is also a massive opportunity for them to make a significant sale which can be invested in other players.
“I’m convinced the deal will happen. Of course, Arsenal fans would like it to happen sooner rather than later because he will be a massive addition to the club.”