The Clarets have tracked the 24-year-old - who can play left wing and left back - over the summer, and, amid interest from Hertha Berlin and, reportedly, Inter Milan, appear to have jumped to the head of the queue with a formal offer which the Bundesliga club are some way from matching at present.
The Ivory Coast international has two years remaining on his contract at Lyon, and is though to prefer a move to Germany, but Burnley have been granted permission to speak to the player, who would help solve the Clarets’ problem area out wide, where they have only Dwight McNeil and Johann Berg Gudmundsson as senior options.
Corner, who scored the opener in Lyon’s Champions League quarter-final win over Manchester City in 2020, has trained only twice this week due to a minor muscle injury suffered in pre-season against Porto a fortnight ago, missing the Ligue 1 opener against Brest.
He is a doubt for Sunday’s game with Angiers.
Lyon are keen for the deal to go ahead, to boost their hand in the market, as they look to bring in the likes of Liverpool wideman Xherdan Shaqiri, while they have also been linked with PSG left back Layvin Kurzawa and striker Sardar Azmoun of Zenit.