The Spaniard who cost the Blues £71.6million appeared to be heading for the exit this summer, after he was dropped for the FA Cup final and a Champions League quarter-final clash at Bayern Munich.
The club have been linked with several goalkeepers over the summer including Edouard Mendy, Nick Pope, Dean Henderson and Jan Oblak.
But Frank Lampard has instead spent £136million on Timo Werner, Ben Chilwell, Hakim Ziyech and Thiago Silva.
Kepa is now convinced his best option is to remain at Stamford Bridge ahead of the 2020/2021 season.
The 25-year-old still has four years left on his £150,000-a-week contract and Chelsea would want to recoup at least £50m of their transfer fee back. This has put off clubs offering him a way out.