The 20-year-old made 29 appearances for Leverkusen in the Bundesliga last season, scoring on three occasions.
The Frankfurt-born midfielder moved to the BayArena from Bayern Munich in 2013 and is set to become Liverpool's second signing following the capture of Rickie Lambert from Southampton.
It is understood that Can has already signed his contract and will be officially unveiled as a Liverpool player on July 1, subject to all the relevant paperwork being completed.
A statement on Liverpool's official website read: "Liverpool FC have today agreed a deal in principle with Bayer Leverkusen to sign 20-year-old Emre Can, subject to documentation being completed."
Can is understood to have had a £9.75m release clause effective for foreign clubs and it is reported Bayern will receive £1.2m as compensation for waiving their buy-back option on the midfielder.
The deal appears to have been agreed on Wednesday night after Leverkusen chief executive Michael Schade confirmed they had received an offer from Liverpool earlier in the day.
"Until Tuesday, it was a rumour," Schade told German newspaper Bild on Wednesday.
"Now I can confirm that an official offer from Liverpool is received by mail."
Schade wished Can every success in the Premier League in a statement on Bayer Leverkusen's official website on Thursday.
"Emre Can has developed very quickly at Bayer 04 Leverkusen over the past 12 months," he said.
"We wanted to keep Emre at Leverkusen but the release clause is part of his contract. So we wish him all the best and lots of success in his time in the Premier League."
The potential acquisition of Can will give Liverpool manager Rodgers greater options next seasons with the club competing in the UEFA Champions League for the first time in five years.
The versatile Germany U21 international is capable of operating in a number of positions across the midfield and defence.
Can, who is also eligible to represent Turkey at international level due to his ancestry, had emerged as a target for Liverpool over the past few months.
He has played under former Liverpool captain Sami Hyypia during the Finn's tenure as manger of Bayer Leverkusen.