The Blues are looking to loan Kepa or recoup the £71m they paid Athletic Bilbao for his signature two years ago.
Dean Henderson, Victor Onana and Jan Oblak have all been touted as targets for Lampard.
But the former Blues midfielder is serious about pursuing Pope, who has been outstanding for Burnley this season.
The England international has the joint-most clean sheets in the Premier League alongside Manchester City's Ederson.
At 28, Pope still has plenty of years ahead of him in goal and looks likely to be considered for England's number spot if he keeps up his form.