The Daily Mail says the 39-year-old Huddersfield Town boss is understood to have met the npower Championship club's owners in London on Wednesday and impressed.
Leicester have also spoken to Roy Keane, while Hull manager Nigel Pearson and former Derby and Nottingham Forest boss Billy Davies have been considered, too.
However, after Wednesday's meeting, Clark - who has led Huddersfield on an amazing run of 41 consecutive matches unbeaten in League One - has emerged as the new favourite to succeed Sven Goran Eriksson. The Swede was sacked last week.
Huddersfield will demand compensation of around £270,000 for Clark and Leicester will back their new boss with a £10million transfer kitty in January as they look to push on for promotion.