Gunners boss Arsene Wenger has admitted the 17 year old is a definite target after a series of impressive displays for the League One club.
Chamberlain, who is the club's second youngest player behind Theo Walcott, already has six league goals to his name from just 24 league appearances.
"We will try now," Wenger said. "We need an agreement with Southampton.
"We need an agreement with the player, and we are not the only ones on the case.
"But we try as hard as we can as I like him as a player."
Alex's father Mark, who played for England between 1982-84, believes Arsenal are the perfect fit for his son's talent.
"Arsenal, with the manager there, the way they play and how they develop players I think they are the ideal choice," he told Sky Sports News.
"I am his dad. I've worked with both. They have both got different attributes. Theo has already played 100 Premier League games for Arsenal, played for England and has scored a hat-trick. He's a really good player.
"Alexander is a little different. He's a bit better technically. He's more of a central midfielder player than a wide player.
"He's coping very well. It's all speculation. It's the time of the year when things do happen. I think if anything is happening the club will keep us notified."