The 17-year-old is regarded as one of the brightest talents outside England's top flight after enjoying a successful campaign last season.
He featured in 34 League One matches last term, scoring nine goals as Saints won promotion to the Championship.
The in-demand teenager is now hoping Southampton do not block his Premier League dream before the summer transfer window closes.
"Southampton, and especially the fans, have been brilliant to me ever since I broke into the first team," said the youngster.
"It has been fantastic helping them to get promoted. But now I feel I'm ready to play in the Premier League."
The likes of Arsenal, Liverpool and Man City are all keen on his signature, but the Gunners are believed to be his preferred destination.
Oxlade-Chamberlain has been likened to the England international Theo Walcott, who made the same move from St Mary's to the Emirates in 2006.