Chelsea doesn't need splash signings

They need squad depth.

And they are focusing on English players because they are a bit out of whack with the FA (or I should say they are up against the limits of homegrown players).

It's why they are going after Ox, Barkley and Drinkwater.

None of them are expected to start, but Chelsea has 7 matches in September and are alarmingly thin (red cards and injuries have exposed this early).

The starting 11 is fine

Morata
Hazard-Willian
Kante-Fabregas
Alonso-Moses
Cahill-Luiz-Azpilicueta
Courtois

It's the depth behind them that his the problem:
Batshuayi
Pedro-Kenedy-Musonda
Bakayoko
Rudiger-Christensen
Caballero-Eduardo

They need more cover other than Batshuayi. It's why they are still making offers being linked to
Belotti and Llorente
Ox, Drinkwater and Mahrez

We shall see what the coming days bring, but I don't expect big name starting XI type players to head to Stamford Bridge. They need squad depth.