The Gunners are 12 points adrift of the Blues with just 14 games remaining.
There is growing unrest at the Emirates with many fans calling for manager Arsene Wenger to leave.
Wenger's contract expires at the end of the season and the Frenchman is yet to commit to another year in charge.
Who could succeed Arsene Wenger at Arsenal?
Wed, February 8, 2017
Express Sport takes a look at top candidates who could replace Arsene Wenger at Arsenal
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Who are the favourites to replace Arsene Wenger at Arsenal?
Arsenal are going through some dark times under Arsene Wenger
George Graham has urged Arsenal to splash the cash this summer
However, Graham has backed the Gunners boss and believes pumping money into the squad could help them challenge for major honours.
"Arsene has set the bar so highly at the club, he's been a breath of fresh air not only for Arsenal but English football," the ex-Gunners boss told talkSPORT.
"Recently they've been off the boil. But the problem is that (although) he's won trophies the league is the one they expect to win.
"Financially they are very stable now but buying could be a problem.
Arsenal slumped to back to back defeats to Watford and Chelsea last week
"They need to buy to players, they have the finances to do it. They've got enough money now to buy the best. They're definitely lacking.
"Some weeks they are outstanding. Every season they put a run together, and they can do it. But they seem at times very vulnerable to smaller teams."
Arsenal have not won the title since 2004.
And failure to win it this season would see their wait stretch into a 14th year.