The Blues finished in fifth spot in the Premier League table to miss out on Champions League football ahead of the new campaign.
The west London side lost 3-0 to Newcastle United in their final Premier League fixture of the 2017-18 season.
Chelsea FC did manage to win the FA Cup thanks to a 1-0 victory over Manchester United at Wembley courtesy of Eden Hazard’s winner.
The Blues still haven’t sacked Antonio Conte despite the manager’s position being under threat throughout most of the season.
Former Napoli boss Maurizio Sarri is thought to be the favourite to take over the Stamford Bridge post.
Ex-Chelsea FC defender Burley believes the Blues risk losing their key players, such as Thibaut Courtois and Eden Hazard, this summer.
“It is a mess,” Burley told ESPN FC. “It is a real worry to Chelsea fans. The fact they are in the Europa League.
“The fact there is no money around at the moment. The worry is they are going to lose key players.”
The Blues have won the Premier League title in two of the past four seasons under Conte and Jose Mourinho.
The west London side signed Everton star Ross Barkley, AS Roma defender Emerson Palmieri and Arsenal striker Olivier Giroud in January.
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