The Reds are returning to Merseyside after a three-match visit of America, which involved tests against established opposition in sweltering weather conditions.
Following the 2-2 draw with Sporting CP in New York on Wednesday night, the team will now move on to Edinburgh to face Napoli at Hampden Park on Sunday before then heading to Evian for a training camp.
"It was an intense period with good opponents and we worked hard to get a better fitness level and to get back in the mood," Matip told Liverpoolfc.com.
"We still have a lot of work to do and we are working hard.