Kepa has failed to impress since his record move to Stamford Bridge from La Liga side Athletic Bilbao in the summer of 2018.
The Spain international has come under intense criticisms from fans and media due to a series of poor performances, and was subsequently dropped to the bench by Lampard in the course of last season.
Many thought Kepa’s future at Stamford Bridge was over when he was relegated to the bench after his poor showing against Liverpool at Anfield in the penultimate game of the Premier League season.
Veteran keeper Willy Caballero was called upon to replace Kepa for the remainder of the season.
The West Londoners are said to be keen on replacing Kepa this summer with names like Ajax’s Andre Onana, Jan Oblak and Edouard Mendy being linked to Stamford Bridge, but it appears the Spaniard will remain as the club’s first-choice stopper.
Bosnich, who played for Chelsea between 2001 and 2003, was asked if this development has surprised him, Bosnich told Sky Sports: “Yes and no.
“I’m a little bit surprised because we talked at the end of last season about it being quite clear that Frank didn’t fancy the goalkeeper.
“No I’m not surprised because of the amount of money that they have spent on all of those other players.
“I’m sure if he could he would go and get another goalkeeper but I’m sure the club will have said ‘hold on a minute, we have spent a record amount on this goalkeeper – let’s give him an opportunity to prove you wrong’.
“If it means they have to go in the middle of the season or the end of next season to get another goalkeeper, so be it. I’m sure that will come into play.
“We have heard that the young goalkeeper who was on loan last season, young [Nathan] Baxter, will come into the frame as well. He could be the answer, we don’t know that.”
He added: “The most important thing for Chelsea is that Kepa performs how he should do and then this talk will just go away.”