The Spaniard was dropped last season after a string of woeful performances and Chelsea are keen on listening to offers for the 25-year-old, who joined the club for a hefty £71m in 2018.
Chelsea are closing in on a £18m move for Rennes stopper Edouard Mendy and it was assumed that the Senegal international would become first choice.
Kepa was in goal as Chelsea kicked off their Premier League campaign with a 3-1 win away at Brighton but question marks were raised over the Spaniard after replays showed he should have done better with Leandro Trossard’s strike.
However, after insisting that there had been no developments over a deal for the 28-year-old, Lampard suggested he was in fact happy to stick by Kepa.
Asked about developments on the club’s hunt for a new goalkeeper, Lampard said: ‘Not at the moment, no. There’s obviously some weeks to go until the end of the window.
‘We’ve got a big squad now so we have to manage that and look at how we move forward in terms of getting the right level of competition within the squad so no news on that one at the moment.
‘I’m very happy with Kepa. I think with the shot I’m not sure if he could have done better but I saw a bit more confidence in how he was playing.
‘I’m happy with him. Kepa is here, he’s our keeper and I’m happy with him. If we are bringing in competition it’ll be competition, that’s the nature of Chelsea. That goes throughout the squad [but] we’ll see. ‘
The club have made six senior signings already this term but Hakim Ziyech, Ben Chilwell and Thiago Silva were not fit enough to feature against the Seagulls.
Chelsea were also without Christian Pulisic after the American felt a slight hamstring pain but Lampard is hoping to have some of his new faces fit next week as the Blues host Liverpool at Stamford Bridge.