According to respected French media partners Infosport and Canal Plus, the players missed a flight from Lyon on Saturday night after a pre-season friendly.
Five of the six players have been named and they are all from South America – four from Brazil and one from Argentina.
Donetsk is right at the centre of Ukraine's current political turmoil, and the tragic Malaysian airlines crash occurred in the region.
All the players mentioned were multi-million pound signings and amongst the team's biggest stars.
Costa has won five titles with the Ukraine club despite still being only 23 and Teixeira has been part of their last four title triumphs.
All five of the players in question are likely to have plenty of suitors in the transfer market should they be allowed to leave, although as none of them have been capped at international level, it is unlikely they would be able to sign for an English club.
Alex Teixeira - Shakhtar Donetsk
- Sports & Recreation
- Alex Teixeira
- Douglas Costa