The battle between Mark Cuban and Cole Beasley over the COVID vaccine is still going strong ... 'cause the Dallas Mavericks owner tells TMZ Sports he's still pushing for the NFL star to get vaccinated.

The two have gone back on forth on social media for weeks over Beasley's anti-vax stance ... and when we got Cubes out in NYC this week, he reiterated he desperately wants the Bills player to get the shots.

"Cole's a good guy, but, you know," Mark said, "getting vaccinated isn't just about you, it's about everybody else as well."

Cuban tells us he believes getting the vaccine is necessary to help protect at-risk people from contracting COVID-19 ... and he REALLY wishes Beasley would change his stance.

"There's 16.9 million cancer survivors in this country," Cuban said. "Three million-plus people who are immuno-compromised. And, when you don't get vaccinated, it's not just about you. It's about other people as well."

Of course, Beasley has dug his feet firmly in the ground on not getting the vaccine ... saying earlier this summer, "I may die of COVID, but I'd rather die actually living."

Beasley has been booed even at home this year in Buffalo over his comments ... but he's remained staunch in his beliefs regardless.