Though the Gunners legend conceded that a late title tilt was unlikely this season, with Chelsea seven points ahead of Arsenal desire the latter's sensational form, Keown did state that the Blues will have taken heed of the impressive run by the North London outfit and will be conscious of them next year.
"Chelsea will win it now but if you ask them next season, they won't fear anyone but they will be aware of Arsenal," said the ex-England defender.
"They will want to challenge next season and they will want to start well next year.
"They need to strengthen in one or two positions but I'm not talking about wholesale changes which some others may have to make if they want to compete."
Keown has been impressed with how Arsene Wenger has improved the squad this season, both with regards to squad strength in depth and how strong they look as a team compared to previous years.
A popular criticism of the Frenchman's Arsenal sides in recent years has been a weakness in defensive positions and defensive midfield, but Keown feels things have been addressed somewhat in these departments.
"They look more convincing as a team than they did last year," he added. "The players look together.
"The squad is better equipped now, Gabriel is putting (Per) Mertesacker under huge pressure and (Francis) Coquelin is in midfield instead of (Mikel) Arteta and (Mathieu) Flamini who are maybe coming to the end of their careers.
"They have a whole array of players who can play off the front and (Olivier) Giroud and (Danny) Welbeck are vying for the centre forward position. The competition for places creates intensity."
Arsenal are set to finish the highest they have in ten years if they maintain their second place position in the Premier League, on the back of a terrific eight-match winning run, while they are also in the last four of the FA Cup, a trophy they are defending having won it last season.