Bale could ignite a white-hot north London derby on Sunday but former Arsenal defender Keown is not sure the Welshman will stay at White Hart Lane.
Bale has been in scintillating form and scored eight times in his last six games for Spurs, including a spectacular winner in Monday's 3-2 victory at West Ham, when he also netted the opener.
The Wales international has seen his stock rise so far he has been mentioned in the same breath as Barcelona's Lionel Messi and Real Madrid's Cristiano Ronaldo.
However, while the spotlight might be on Bale and his left boot on Sunday at White Hart Lane, Keown, who played a key role in the Arsenal defence for more than a decade, says the focus for managers Arsene Wenger and Andre Villas-Boas will be securing a win which could help them book their place in the Champions League.
"Tottenham want to get into the Champions League. Of course they want to have bragging rights but first and foremost they want to get into the Champions League and that is up for grabs," said Keown.
"If Tottenham are going to keep Gareth Bale they will have to fulfil all of his aspirations for what he wants to achieve and get into the top four. Someday they might have to deal with him wanting to leave if they don't start winning things.
"If Arsenal win they will be one point behind Tottenham and that is what Wenger will be focusing on.
"Certainly, being in the Champions League helps with money and is a draw for signings in the future. Arsenal will want to keep progressing as a football club. That should not be taken for granted."
Keown, who is a supporter of the FA Community Awards which recognise the importance of grassroots football, has experienced several fiery derby games against Spurs, none more so than the 2-1 defeat by Tottenham in 1999 when he was shown a red card as the contest bubbled over.
The former England international expects plenty of that passion on Sunday as both Wenger and his players will want to bring Bale down a peg or two.
"Tottenham are very good with the in-form player in the Premier League at the moment in Gareth Bale. He looks sensational and like a player that is totally enjoying himself and finding out how good he is," Keown said.
"He started as a left-back who had an incredible record of when he played, Tottenham never won, but now he has turned it on its head.
"Wenger knows the strengths and weaknesses of his opponents.
"It will be a white-hot atmosphere and Arsenal will need to defend for long periods.
"Professional pride means you don't want someone else to be the top man. There will be plenty of other teams who can't stop Gareth Bale and you can't just focus on one player as they have got other threats, like Moussa Dembele, Jermain Defoe and Emmanuel Adebayor."
Keown also hailed the impact of Spurs manager Villas-Boas, who would lead Tottenham back into third place behind the two Manchester clubs with a win on Sunday after Chelsea's victory over West Brom bumped them down into fourth.
"There is a really good spirit at Tottenham," Keown said.
"They have a togetherness and Andre Villas-Boas looks as if he has the respect of the players. It seems very different from the outside looking in to when he was at Chelsea.
"Gareth Bale only got one assist last season but he has 11 so far this season. Villas-Boas has encouraged him. Harry Redknapp gave him self confidence but Villas-Boas is getting more out of him.
"It is all about the timing and the player has more belief in himself. It is great to see a player fulfilling his potential."