Chelsea finished fifth in the Premier League though won the FA Cup and will compete in the Europa League next season.
Lifting the trophy at Wembley earlier this month was Chelsea’s 15th major competition success in as many years.
And though they won’t take their seat at the top table of European football, Azpilicueta believes Chelsea’s rich recent history will still attract top names.
“Of course big players will still want to come to Chelsea because we win lots of silverware,” Azpilicueta told Evening Standard.
“I have no doubt that the club will get a squad that can compete to win for trophies. I am sure that will happen.
“If the club decides that we need to get players in, I’m sure we will get the quality we want.
“It was important to win this season with a trophy. It shows we are still winners. When the results are not there, people look for something else.”
Chelsea are continuing their transfer business despite ongoing speculation over the future of manager Antonio Conte.
The Blues are rumoured to be interested in Napoli boss Maurizio Sarri should Conte leave Stamford Bridge.
However, Express Sport understands Napoli are holding firm over a release clause for their ex-boss, which Chelsea are not keen to pay.
Should Sarri join the London club, he would be their sixth manager from Italy.
Chelsea FC tracking 30-year-old South American but face PSG interest – report
Chelsea FC are set to battle it out with Paris Saint-Germain to sign Gonzalo Higuain, according to a report in Italy.
Italian media outlet Tuttosport, as quoted by talkSPORT, is reporting that the Blues are interested in a potential deal to sign the Juventus striker.
The same article states that Chelsea FC have been put on red alert after Juventus expressed a desire to cash in on the South American forward this summer.
According to the same story, the Serie A champions want to sell the Argentina international given the striker is 30 and entering the twilight of his career.
Higuain has won two Serie A titles and two Coppa Italia titles at Juventus since his move from their title rivals Napoli in 2016.
The Argentinian striker comes with a wealth of experience having spent seven seasons at Real Madrid before his move to Naples.
Higuain won three La Liga crowns and the Copa del Rey during his spell at Real Madrid and scored 121 goals in 264 appearances in all competitions for los Blancos.
The 30-year-old was part of the Argentina team that lost 1-0 to Germany in the World Cup final in Brazil in 2014.
Chelsea FC finished in fifth place in the Premier League table last term.