Francesco Guidolin will be given time to shift Swansea’s momentum after a five-match winless run.
An American consortium led by Stephen Kaplan and Jason Levien took over in July, inheriting Guidolin as manager.
But it is understood a change of boss just weeks into the Premier League season is not inevitable, despite Swansea being without a win since the opening day.
Ryan Giggs and Gianfranco Zola are among those to have been linked with the Swansea job, but Guidolin said after Saturday’s loss to Manchester City that he had not met with club chairman Huw Jenkins to discuss his future.
Positive signs were evident in defeat to leaders City, but Swansea’s only wins this season were at Burnley and against Peterborough in the EFL Cup.
And with Swansea playing Liverpool and Arsenal either side of the October international break, the situation could deteriorate before it improves for Guidolin.
The former Udinese boss joined Swansea in January as head coach and was given a two-year contract in May.
Giggs, who left his role as Manchester United assistant manager over the summer, ending a 29-year association with the club, last week said he had had no contact with Swansea.