Christian Eriksen missed Brentford's 2-1 defeat to Leicester on Sunday afternoon after testing positive for Covid-19.
The 30-year-old midfielder has made three appearances for the Bees since joining the club on transfer deadline day in January.
Earlier this week he was called up to the Denmark squad for the first time since suffering a cardiac arrest while playing at the European Championship last June.
Denmark will play two friendlies during this month's international break, travelling to the Netherlands on March 26 before hosting Serbia three days later.
Speaking after Brentford's loss at the King Power Stadium, Thomas Frank was optimistic that Eriksen would still be able to play a part in these games.
'[He was] not quite right,' the Bees manager said. 'You need two negative tests and a medical test. Hopefully he can travel with the national team.'
Meanwhile, a statement from the Danish FA read: 'We have been in ongoing dialogue with Christian and Brentford about the situation. We expect to see Christian as soon as possible during the week. We look forward to having him and expect to have him against the Netherlands and Serbia.'
Brentford have won both of the two games that Eriksen has started so far and the midfielder provided an assist for Ivan Toney in the 2-0 victory over Burnley last weekend.
Iranian winger Saman Ghoddos has also tested positive for Covid-19, putting his own upcoming international commitments in doubt.