Kepa arrived in England from Athletic Bilbao as the most expensive goalkeeper in the world in the summer of 2018.
The Basque-born star has come under intense criticisms from fans and media due to a series of poor performances.
Kepa was dropped to the bench by Frank Lampard after his poor performance against Arsenal in January but regained his position in early March after a slight improvement in wins against Liverpool and Everton in the FA Cup and Premier League respectively.
The Spaniard’s ability has been questioned again in recent weeks particularly in Chelsea’s seismic defeat against Liverpool at Anfield.
Willy Caballero was called upon at the expense of Kepa in Chelsea’s final game of the league season against Wolverhampton Wanderers, where the Argentine kept a clean sheet in a 2-0 win.
Bosnich has suggested that Kepa’s days in West London are numbered during an interview with English news outlet Sky Sports.
"When a big club that has been challenging for honours purchase a goalkeeper it’s for right there and right now," the Australian said.
"He hasn't had a particularly good season and the bottom line is you have a fall-out with the manager in any kind of way, it's a slippery slope.”
"So I can fully understand Frank wanting to basically take that level up and to say 'look, listen, he's just not for me, I want somebody else'.
"If that's the case then there's going to be an issue as the club shelled out so much money for him. I don't think they'll be able to recoup that money, they may be able to recoup some.
"And of course the goalkeeper can make it very difficult for Chelsea by saying that if you are going to sit me out of the team then I'll stay here on these massive wages and run down my contract for nothing.
"They've got a big decision to make. I think it's quite evident from what we've seen, and the fact that he didn't play in that last game of the season, that he will be on his way."
Chelsea conceded 54 goals in the just ended Premier League season with Kepa conceding 46 of those.
