The £40million Spanish fullback lost his place at Chelsea last season to Emerson Palmieri in an unhappy year for the former Real Madrid star – Alonso was even an unused substitute in Chelsea's Europa League final win over Arsenal in May, and he was linked with a move to Atletico Madrid this summer.
Alonso said on Friday: “I signed a new contract last year. I'm very happy here and I don't know if there has been any contact with Atletico.
“You'd have to speak to (Chelsea director) Marina Granovskaia for that.
“Of course it was a frustrating time last year. I would love to play every minute - but things happen. Now it's a new season.
“I have four more years here. The last few years have been amazing and I want more of that. I want to be playing, to keep winning things."
The ex Bolton defender revealed he has not yet spoken to Lampard about his future – but labelled ex manager Maurizio Sarri's style of football “unique."
He said: “The new manager has not spoken much. We're training hard.
“The style will definitely be different. Last year was a unique style in terms of what Sarri wanted. Now it's another thing.
“We're all very excited. It's been a tough first couple of weeks but this is the time to get ready. I'm very motivated to start well.
“It's different with every manager. Each has his own method. We are training very well, high intensity, lots of fitness. Trying to get his ideas and to get better.
“It's a fresh start for everyone. Last year is part of the past and now I just want to keep working, enjoy playing and help the team win.
“We have to go for everything. It's early to talk about targets, but we have to think to go for everything. Make sure we are ready for the start. The quality is there and if we work hard we can have another good season and try to be top of the table."