Draymond Green is happy to settle his feud with Tristan Thompson, so long as any meeting between the pair does not hit him in the pocket.

Emotions were running high at the end of the opening game of the NBA Finals on Thursday, with a scuffle breaking out in the closing stages of the Golden State Warriors' overtime triumph over the Cleveland Cavaliers.

Thompson appeared to shove the basketball in Green's face after being ejected for elbowing Shaun Livingston, with the Cavs forward fined $25,000 by the league for his actions.

He also pointed outside while leaving the court and, while unwilling to back down from the challenge, Green has no intention of losing money just to settle the score with his rival.

"I can't meet him outside of [the arena], because I'll still get fined," the three-time All-Star told the media ahead of Sunday's game two.

"But I can meet him in the streets any day. So you can say [that] somebody [should] meet you at the [team] bus, [but] I'm not [going]. I'm going to keep taking care of my family. I'm not going to meet you at the bus.

"But you know [in] the summers, you can meet anybody anywhere. So all that, 'Meet me outside, meet me at the bus,' like I ain't interested in giving up no money for that. But if you want to see me somewhere else, that's fine - any time."

Green went on to explain it is expected emotions will be high in a series when both teams are desperate to win the title.

"You're trying to win a championship, so there should be emotions involved," Green said.

"And if not, then whoever's emotions aren't involved should go sit down somewhere. This is what you work your whole life for, so it should carry over."