Kidd has been linked with the role and could be handed a short-term deal by chairman Dave Whelan, who is desperate to see the club return to the top flight at the first time of asking.
Wigan started the campaign as one of the favourites to achieve automatic promotion, but are currently six points shy of the play-off positons.
A source confirmed that Kidd would be given permission to talk to Wigan if Pellegrini found a suitable replacement, adding: "Brian is very popular at the club but his role has changed since the departure of Roberto Mancini.
"Brian and Roberto shared a special bond but even though he was retained by the new management, he spends more time in the background and doesn't have as big an influence.
"The main benefit is obviously the fact that he is English, and is a go-between for the English players. But as long as the current manager could line someone up quite swiftly, it would be a surprise if the club prevented Brian from spreading his wings."
Source: Manchester City MAD