Jones and attack coach Simon Amor have been identified as close contacts of Proudfoot and must self-isolate for 10 days.
In a statement, the Rugby Football Union said Proudfoot was not displaying any symptoms of the disease.
The England squad are due to meet at St George's Park on Wednesday, 27 January to prepare for the Six Nations.
The rest of the England staff are scheduled to arrive two days before that, with Jones and Amor attending meetings virtually.
Defence coach John Mitchell is expected to be available to hold face-to-face sessions with the players.
Following a further negative test, Jones and Amor will be able to join up with the squad on Thursday, 28 January.
It was confirmed on Monday that coach Jason Ryles will not join up with the squad having chosen not to re-locate from Australia to England this month because of the Covid lockdown.
Jones will confirm his 28-man squad on Friday, with England scheduled to start their Six Nations campaign against Scotland at Twickenham on 6 February.