Justin Bieber and Indians pitcher Shane Bieber have bonded on social media due to their famous last name -- and they even wore baseball jerseys recently jokingly paying tribute to the other.

Shane wore a "Not Justin" jersey during MLB Players' Weekend, when the athletes get to wear whatever name they want on their jerseys. And, Justin responded by rockin' a "Not Shane Bieber" jersey during a recent motorcycle outing.

Now, we're told the team wants to take the bromance to the next level by trying to arrange a face-to-face next week when the Indians come to California for a 3-game series with the Angels.

Our sources tell us reps for the Indians have reached out to Justin's camp to invite him to one of the games so he can meet Shane ... and we're told JB is seriously considering the offer.

Justin is a big sports fan and loves hanging with athletes ... from Neymar to Floyd Mayweather and he's also obsessed with hockey.

Shane has previously told us interacting with Justin on social media was one of the great thrills of his life!!!