Famagusta District Assistant Police Chief Georgios Economou said witnesses described the two suspects as appearing to be foreign nationals.
Checkpoints and airports have been put on alert, he added.
For recent transfers, see List of Cypriot football transfers summer 2016.
Another friend, Ollie Ellis, wrote on Facebook: "Last night we lost one amazing member of the Ayia Napa family and a very good friend of mine.
Investigators have been able to track some of the suspects' movements through CCTV cameras, he said, adding that authorities at all airports, ports and crossing points into the breakaway Turkish Cypriot north of the ethnically divided island have been warned to lookout for the suspects.
Mr Barker, 22, had knife wounds to his back in the attack in Grigori Axfentiou Street, but survived.
Ayia Napa played in their grounds wnen in 2nd division and friendlies. For sure they play in Paralimni stadium this season. I am a keen football fan and know for sure.
Price is decided last week but against Omonia prices are bit high , my guess 17e
The Foreign Office said it was providing support to Mr Low's family.
"Words can't describe how much of a shock this is.
His friend, who is also 22, was stabbed four times in the back. He is expected to make a full recovery.
They actually use both stadiums cylib ......I know I've seen them play at it many times!
Ayia Napa FC plays its official games in Paralimni stadium this year as Ayia Napa stadium does not fit the demands for 1st division.
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She said he and Mr Barker had been due to fly home later the same day.
Police have also issued a warrant for a third man suspected to have helped the suspects escape to the Turkish-held north of the holiday island.
The biggest achievements of Ayia Napa FC's history was in season 2005–06 after it finished 3rd in Cyprus Second Division and was promoted to the Cypriot First Division also in the 2014–2015 season it avoided relegation for the first time in its history.
Mr Low's mother, Helen, 47, has said her son, a former club manager at the resort, was not an aggressive person and had simply been "in the wrong place at the wrong time".
A row is said to have broken out before Mr Low and Ben Barker were stabbed.
The suspects were described by Cyprus Police as young. The first was "short, chubby" and wore jeans and a white shirt while the second was also said to be short, with short black hair and was naked from the waist up.
Athlitikos Omilos Ayia Napa (Greek: Αθλητικός Όμιλος Αγία Νάπα, "Athletic Club Ayia Napa") is a Cypriot football club from the town of Ayia Napa. The club was founded in 1990 after the merger of two clubs: APEAN (Athlitiki Podosfairiki Enosis Ayias Napas; "Athletic Football Union of Ayia Napa") and ENAN (Enosis Neon Ayias Napas; "Youth Union Ayia Napa").
Estate agent George Low, 22, from Dartford, was stabbed in the neck near a nightclub in Ayia Napa on Sunday.
Only way to get there is by taxi but is a very short distance from Protaras. Omonia has many fans and you might only get tickets on Ayia Napa's side
The group did not know each other beforehand, Mr Economou added.
The 48-year-old woman who has been taken into custody pending further inquiries - but has not been charged - is said to be the girlfriend of Mr Akpinar and is accused of taking him a fresh pair of clothes and retrieving his mobile phone.
Tributes have been paid on social media with Niamh Rose writing: "Rest in peace George Low you've touched the lives of so many."
(Thanks to friend that helped me wite informetion for a game in larnaca but i think we could not make it)
The team's stadium is Municipal Stadium of Ayia Napa, which is a multi-use stadium in Ayia Napa. It is currently used mostly for football matches and holds 2,000 people. However the stadium was not suitable for first division matches, so for the season 2006–07, when Ayia Napa plays in First Division, the team is using for home the Tasos Markou Stadium in Paralimni.
Ill want to watch a home football game of aya napa f.c against OMONOIA LEFKOSIAS on 27/9 wite my 2 boys (11,6)
Arrest warrants have been issued for two Turkish Cypriot men, Mehmet Akpinar, 22, and 42-year-old Sali Ahmet.
The Ayia Napa Stadium where the game is played sits just above Ayia Napa get a bus to Ayia Napa & then very short taxi ride. Or taxi direct for approx €20
A woman who appeared at Famagusta District Court in connection with the case told Cypriot police the attack was triggered after two British men were seen urinating, the court heard.
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"You have been taken from us in one of the worst possible ways."
A district court in Larnaca remanded her in custody for eight days.
A GoFundMe page, set up by friends to help pay for his funeral, has so far raised £5,000.
Were is the stadium ? How far from anastasia beach in protaras ? How much coast tickets ?
Mr Economou added that the two victims had worked during the previous two years in bars and clubs in the area but the wounded Briton told investigators that he and Mr Low had been on holiday this time.
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