The former defender believes choosing a full strength squad for the Watford game suggests Arsene Wenger wants to win the title.
The Gunners ran out as 3-0 victors at Vicarage Road to remain second in the table and continue their impressive form, and did so with arguably their strongest eleven on the field.
A game against a newly promoted side could have been the perfect opportunity for Arsene Wenger to rest his big stars with a huge Champions League clash against Bayern Munich upcoming in midweek, and Winterburn says not doing so shows he may be focused on trying to win the Premier League title.
"Maybe he believes his team is capable of challenging for the Premier League," Winterburn told Sky Sports.
"That's the competition he always talks about as being No 1 because it's consistency over 38 games. The Champions League is very important, but if you could give him one over the other, I'd say he would take the Premier League."
Wenger’s side were hotly tipped to be potential title challengers before the start of the season having secured their second successive FA Cup triumph at the end of last season.
A disappointing summer transfer window saw them failure to add any outfield players though, with Petr Cech their only capture, leaving some questioning if they had a squad capable of competing for the title.
Winterburn believes they do though, saying that they must be within three or four points of the leaders in April to be in the title race.
"I believe Arsenal have got the squad, on the second half of last season's form, to challenge for the title,” he added.
"A title challenge is either leading or being within three or four points of the leaders in April. That's a title challenge, not in January and February. I'd love them to be there to see what happens, put the players under pressure to see if they can cope, but there are other teams that people will say have got stronger squads."