The defending Premier League champions crashed out of the FA Cup on Saturday evening after a 2-0 defeat by Everton.
Chelsea have endured a tough week after Paris Saint-Germain’s 2-1 victory over the Blues eliminated from the Champions League on Wednesday night.
The west London side are 11 points behind fourth-placed Manchester City in the race to secure a place in next season’s Champions League.
Although the Blues will more than likely be unable to offer premier European football next season, former Arsenal midfielder Parlour believes the Gunners will still be able to attract top players to the Emirates Stadium.
“Chelsea can still pay big money,” Parlour told BT Sport.
“Paul Pogba may not. You’d still get some of the Dortmund players. They’d come to London and the Premier League.”
Former Chelsea striker Romelu Lukaku scored twice in the final 12 minutes to secure a brilliant 2-0 win for the Blues.
The defending champions will host London rivals West Ham United in their next Premier League game on Saturday 19 March.
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