Coach Fabio Capello makes his decision on the England captain in August - and the two main contenders were involved in angry exchanges at Stamford Bridge on Saturday.
Ferdinand in particular appeared to lose his cool towards the end of United's 2-1 defeat and is reported to have apologised to a female Chelsea steward he accidentally kicked in a fit of rage after the final whistle.
Sir Bobby Robson: "The sight of those two towering leaders, John Terry and Rio Ferdinand, squaring up to each other illustrated to me the passion and endeavour of both players.
"As a former England manager, I would tell Fabio Capello not to be concerned at all with the brief shoving between them. It shows their desire to win and, when they wear the white of England together, they will be a formidable partnership.
"Ironically, they are regarded as the main candidates to be Capello's England captain. I think they showed yesterday that either one of them will do the job rather well."