The Reds travel across the Atlantic following their final domestic friendly clash with Huddersfield Town on Wednesday night.
This will see them take in clashes with Chelsea (July 27), AC Milan (July 30) and AS Roma (August 1), before returning to England to take on Barcelona at Wembley Stadium (August 6).
Matip was thought to be a doubt after limping off late on during Liverpool‘s 2-0 win away to Wigan Athletic on Sunday.
But after a scan on his ankle, it has been revealed that Matip has suffered no serious damage.
Therefore, while he may miss out at the John Smith’s Stadium, the Cameroon international is fit to join up with Klopp’s squad for the rest of pre-season.
This is a major boost to the German, who has already seen Mamadou Sakho and Joe Gomez drop out of his centre-back ranks for the summer, with the pair suffering from Achilles injuries.
Meanwhile, Tiago Ilori is set to join up with the Portugal squad at this summer Olympic Games in Brazil, leaving Klopp with just three senior centre-backs.
After a fee of around £4.2 million was agreed between the two clubs, Estonia captain Klavan is set for a medical with the Reds on Tuesday.
Klavan will likely play fifth choice to Sakho, Matip, Lovren and Gomez in 2016/17, with both Ilori and Wisdom set to leave the club during the transfer window.
Matip has already shown strong signs of progress in Klopp’s back line during pre-season, after making the switch from Schalke this summer on a free transfer.
The 24-year-old’s height, strength and agility make him a great option at the back, while his excellent passing range will suit Klopp’s direct brand of attacking football.