The 38-year-old was brought into the Chelsea side for their crucial final Premier League game of the season against Wolves and kept his place in the FA Cup final and against Bayern Munich.
With Arrizabalaga dropped for a second time this season, speculation is rife that Lampard will look to sell him this summer despite costing a club-record fee.
The likes of Dean Henderson, Nick Pope and Andre Onana have all been touted as possible replacements.
It was another tough night for Chelsea defensively as they shipped four more goals against Bayern Munich, crashing out of the Champions League 7-1 on aggregate.
With Caballero now firmly established as the club’s number one goalkeeper with only five weeks until the start of the new season, the Argentine has opened on his dismantling Arrizabalaga un goal.
“I’m contracted one more year at this club. I’m really happy to play in this t-shirt,” Caballero told BT Sport.
Why should you sign up?
In each football.london Chelsea bulletin, we’ll be bringing you the latest breaking news, transfer features and comment pieces, as well as the key talking points for fans.
We’ll also send special newsletters when big stories break or there’s a special event happening.
How do you sign up?
It’s easy and only takes seconds.
Simply type your email address into the box at the top of this article – or any article on the Chelsea section of football.london in fact – labelled ‘Get the biggest daily stories by email’ and click ‘Subscribe’.
And that’s it, you’re all set.
If you decide later that you no longer wish to receive the emails, simply follow the unsubscribe link in one of the newsletters – but we don’t think you’ll want to.
For more details, click here.
“I’d like to keep playing. I’ve become the first option, the first choice, and we’ll see what happens in the future. I’ll keep working hard to have this opportunity again.
“The boss said I had to play these couple of games. I’ve been in the second position as a goalkeeper, but I’ve always trained with the mentality of a first choice.”