At least, that's what the rapper says -- 'cause when he grabbed baseball's top free agent backstage at the Florida Georgia Line concert Saturday ... he gave his best St. Louis pitch.

"Listen, Bill, Mr. DeWitt, call me! I got this. Alright? I'm doing all the negotiations. He just need a little convincing, man! That's all!"

Bryce's response -- he didn't say no!!

Of course ... Bryce has a TON of suitors these days -- even ones just as famous as Nelly ... 'cause when he hit the FGL concert with his old pal, Kris Bryant -- you know Cubs talk went down there too.

Bryce is playing his free agency card close to the vest -- with the Nationals, Phillies, Cubs, Cardinals, Yankees and more all being rumored to be his next spot.

We spotted Harper in L.A. a few weeks ago and he hinted that the Cubs and White Sox could have an edge because Chicago is his favorite city ... when it comes to restaurants!