Nigel Pearson's decision to send Chris Martin to Fulham meant McClaren always faced an uphill struggle at Derby County.
Carvalhal is under pressure from some Sheffield Wednesday supporters.
The former Derby County manager has been linked with the vacant managerial post at Middlesbrough.
Middlesbrough have parted ways with manager Aitor Karanka.
Middlesbrough sacked Aitor Karanka on Thursday, with the former Chelsea and Derby County bosses in contention to replace him.
Pearson, who has reportedly thrown his hat into the ring to become Norwich City's next boss, signed James for Leicester City five years ago.
Former Derby County manager Nigel Pearson is reportedly being lined up to replace Birmingham City manager Gianfranco Zola.
Leicester City have sacked manager Claudio Ranieri - less than a year since winning the Premier League title.
Aston Villa fans have been taking part in a HITC Sport poll on who they want to see in charge of the club next season.
Derby County won just three times under Pearson as his managerial reputation took a substantial hit.