Lampard, who is Chelsea's al-time top goalscorer, took over as Blues boss after Maurizio Sarri's Juventus departure.
There's no price mentioned, but considering Chelsea wanted €40m overall from Milan (€5m for the loan and €35m to buy him), you'd expect the Blues to want something similar after a good season. The Chelsea captain believes that feeling is massive.
Lack of fitness, and perhaps a so-far unembedded "Lampard-system" were evident, and gave reason for Chelsea's shortcomings, but Keith Long's Bohemian's showed they were no pushovers, as a late Eric Molloy equaliser was enough for the Irishmen to grind out a result and put a small dampener on the Lampard homecoming party.
"We have great support over here and we've seen that at the hotel every day with the fans coming to see us", he said.
Kovacic, who was on loan at the Blues last term, was able to join permanently due to him already being registered as a Chelsea player.
"We won the Europa League, we finished third and his [Sarri's] choice was to move on, to go back to Italy".
With a transfer ban looming over the club and the loss of Eden Hazard to Real Madrid over the summer, questions were asked about hiring an unproven manager. 'In those moments we couldn't imagine a Chelsea side winning a trophy without those quality players.
"I'm looking forward to working with [Lampard] a lot - he was an incredible player and he showed last season that he is a good coach as well".
"But every year we've had the chance to bring trophies back to the Bridge".
But Azpilicueta is optimistic Lampard's experience as a Chelsea player will make up for his inexperience as a manager.
"I'm sure his desire, his passion, for being a manager to have this chance to be the manager of Chelsea - the club that he loves and the fans love him - everyone at the club is very excited and the only way we can get it started is by winning".
In that same time, every Chelsea central midfielder has scored at least once - including forgotten man Danny Drinkwater.
"We've only been back just a few days so there had been some pressure on the lads and we have been working them very hard". We will work hard because we have an exciting season ahead, new challenges and the only way to prepare it is by working hard and getting success at the end of the season.