The two sides face off in tomorrow's big North London derby, but Spurs are currently in turmoil after consecutive thrashings at the hands of Chelsea and then Benfica.
The pressure is piling on manager Tim Sherwood, and with fans desperate for success, Keown - who spent 16 years as a player for Arsenal over two spells - says that Spurs need to take a look at how Arsenal have been continually in the top four, and pointed to the faith shown in manager Arsene Wenger.
"I know Arsenal haven't won a trophy in nine years but there is stability right through the club. The new stadium, the development of young players, the trust in the manager, all of those are in place. That is not true of Tottenham."
"Yes, there is a new stadium in the pipeline, and they have produced some good young players. But when there is so little consistency with the management how can you expect to progress? The Arsenal board trust Wenger and he trusts his players. It's difficult for Sherwood because there is such uncertainty about his long-term future."
Sherwood is an inexperienced manager who took over from Andre Villas-Boas in December, and Keown had some words of advice for the beleaguered Tottenham boss regarding the playing time of young England international winger Andros Townsend, suggesting he should be used like Wenger uses Alex Oxlade-Chamberlain.
"He revitalised Emmanuel Adebayor, but I think he's missing a trick with Andros Townsend. Roy Hodgson showed faith in Townsend and was repaid with excellent performances.
Arsenal's Alex Oxlade-Chamberlain was superb against Bayern because Arsene Wenger backed him. Sherwood needs to do the same with Townsend."
Keown's comments come despite him never having been a manager, and whilst it's unlikely that Sherwood - or Spurs chairman Daniel Levy - would necessarily listen to an ex-Arsenal hero, some stability at White Hart Lane is needed and the anticipated replacement of Sherwood in the summer is a huge moment for the club, as they need to hit on the next appointment.