Walcott will be free to sign a pre-contract with a foreign club from tomorrow.
"Even with the speculation going on, he's stuck to his task. He's been a great professional ," said team-mate Oxlade-Chamberlain.
"He's a good lad in the dressing room and we need him to keep doing that for the rest of the season. We've all been giving him a bit of banter (about his future) but that's for Theo's people to sort out."