The 38-year-old is also believed to be under consideration by Manchester United if they decide to make a change with Erik ten Hag’s future in doubt.
McKenna – who is contracted to Ipswich until 2027 – is ambitious and is understood to be keen to take the next step in his career.
Talks with Ipswich are likely to take place this week and the Tractor Boys are expected to offer McKenna a new deal to convince him to stay at Portman Road.
Chelsea are believed to be in pole position, despite Brighton’s interest, with United’s situation adding to the complexities as they are yet to confirm what will happen with Ten Hag.
Any club will need to pay at least £4m compensation to take McKenna and Pert.
There is no panic from Ipswich, they are calm and recognise this comes with the territory after McKenna’s stunning success in taking them back to the Premier League for the first time since 2001-02.