The Sun says Jewell will be Middlesbrough's target if Southgate fails to turn round their fortunes by next month.
Southgate is under pressure as boss having won only twice in 12 Premier League games.
And there are huge concerns about the swathes of empty seats at Boro.
Just over 25,500 turned up to see the 1-1 draw with Spurs - 10,000 short of capacity.
Jewell stepped down as Wigan manager at the end of last season.