The left-back fell ill after flying to Slovenia for his country’s opening Nations League and was immediately quarantined.
He then didn’t train with the rest of the team for three days and reports coming out of Greece claim that he has Covid-19.
A statement from the Hellenic Football Federation confirmed that a member of the Greek national football team had tested positive but didn’t name the player.
According to Greek outlet SPORT 24, that player is Tsimikas, who took a test carried out by UEFA, before the rest of the squad did the same.
The results of the other tests will reportedly be released on Saturday before Greece travel from Ljubljana to Pristina ahead of their second Nations League game against Kosovo.
A statement from the Hellenic Football Federation read: "The Greek Football Federation was informed today of a positive COVID-19 sample on the results of checks carried out by the authorised by UEFA medical service among members of the mission of the national men's team, which is located in Ljubljana and preparing for Sunday's match with Kosovo in Pristina.
"UEFA's protocol is being adhered to and EODY [Hellenic National Public Health Organization] as well as the GGA health committee were immediately informed.
"The member of the squad who had a positive sample and was isolated for the last 36 hours for precautionary reasons from the other members of the squad, leaves the team tomorrow morning, while the preparation of the Greek team continues.
"The other members of the squad underwent a new test today in accordance with the UEFA protocol and the results will be announced tomorrow before the departure of the team to Kosovo."
Tsimikas joined Liverpool from Olympiakos only a few weeks ago with Jurgen Klopp keen to bring in some back-up for Andrew Robertson at left-back.
Robertson claimed earlier this week that he is ready to rise to the challenge of the competition posed by the 24-year-old.
“He’s settled in very well. You can see him growing in confidence as a player and as a person in the squad and I think that’s credit to all the lads and all the staff,” Robertson told Liverpoolfc.com.
“Look, we’ve all been there, we all know how daunting it is walking into a new changing room and not knowing anyone and things like that, but I think we all know how that feels and we’re all very cautious of that so we try to make people feel as welcome as they can and as quickly as they can because the quicker you get the person out of his shell, the quicker you get the player out of his shell. I think that’s what’s happened.
“I’ve seen him in training and he looks a really good player. I can’t say I saw much of him playing for Olympiacos and things like that but it’s up to the club and they’ve obviously seen something there that can improve the squad and I’ve got no doubt he will do.
“For me personally, he’s obviously in my position and I want to stay the number one left-back. I want to play as many games as I can, to stay fit, to keep my levels high and I want to be playing every game.
"I know that’s not always possible but that’s my attitude going into it and it’s up to me to keep putting in performances and hopefully stay number one left-back.”