Celtic may still be eyeing up other managers this summer.
West Bromwich Albion parted company with Darren Moore last month.
Clarke previously turned down an approach from Fulham.
Nikola Katic made a rare Scottish Premiership start as Rangers were held 1-1 by Steve Clarke's Killie at Ibrox on Saturday.
Connor Goldson escaped a red card for Ibrox side Glasgow Rangers on Saturday, says Steve Clarke.
Fulham need a new manager after sacking Claudio Ranieri with reports saying the Premier League strugglers want Moyes, David Wagner and Steve Clarke.
Premier League strugglers Fulham are reportedly eyeing Moyes, Wagner, Bristol City coach Lee Johnson and Kilmarnock boss Steve Clarke.
Kilmarnock boss Steve Clarke has been mentioned as a potential replacement for Brendan Rodgers at Scottish Premiership champions Celtic.
Kilmarnock's Steve Clarke has shot down any talk of him going to Celtic.
Rangers are currently sitting two places about Steve Clarke's Kilmarnock in the Scottish Premiership.
The Reds will face Suarez's Barca should they overcome Porto in their Champions League quarter-final second leg.
Sheffield United are attempting to catch Leeds United in the race for promotion, but they are currently three points behind Marcelo Bielsa's men.
Leeds United fans still admire ex star.
Tottenham Hotspur currently hold a one-goal advantage over Manchester City ahead of their Champions League encounter on Wednesday night.
Mauricio Pochettino's Tottenham Hotspur side are due to face Manchester City in the Champions League later this evening.
Liverpool midfielder Fabinho has been in excellent form for Jurgen Klopp's side of late.
Mauricio Pochettino's Tottenham Hotspur side have a 1-0 lead to protect ahead of their match with Manchester City tomorrow.
Leeds United and Sheffield United are fighting for an automatic promotion spot.
Tottenham Hotspur still have a perfect record in their new stadium, with Mauricio Pochettino's side back on track now.
Leeds United, Norwich City and Sheffield United are aiming for automatic promotion to the Premier League.
The former West Brom manager is not happy to see his former player struggling.
Outside of the favourites like David Moyes, Nigel Pearson, Brendan Rodgers, Sean Dyche and Steve Bruce, who else could the club potentially sound out to replace Remi Garde?
The Bradford City boss is still a hero at the Berkshire club.