The Olympiacos star completed a quick transfer to the Reds this week.
The Greece left-back will now compete with Andy Roberston for a starting spot after the £11.75 million transfer.
And Greek outlet Sportime says Klopp told the 24-year-old before the deal was concluded: "The decision is yours.
"We want you, you fit very well in our project and in how we want to play."
Tsimikas will be hoping to get a lot of game time next season, even though he is currently second choice behind Roberston for the left back spot.