Head of investment Peter Harrison is reported to be in the frame to replace Dobson, with the confirmation expected to coincide with the release of Schroders’ full year numbers.
A spokesperson for Schroders said: “We don’t comment on market speculation and rumour.”
Dobson, who is 63, has been in the post for 14 years.
Schroders shares have not moved significantly today, trading up 1.4% at 2726p.