Mr Schlee said: "We used to wait for people to come to us, but we're reaching out to more British labour applicants through social media and jobcentres."
Pret, which last year created 839 full-time jobs, recently revealed it is launching a programme this summer to offer 500 week-long paid work experience placements to UK school students.
Mr Schlee said he was "encouraged" by Government plans to head off recruitment woes for the hospitality industry with a new "barista visa" mooted to allow young European citizens to continue coming to the UK to work in coffee shops and pubs.
His comments came as the group posted a record set of full-year results, with worldwide sales rising 15% to £776.2 million in 2016, while operating profit grew 11% to £93.2 million.
Like-for-like sales rose 4.8%.