The 17-year-old Argentine forward - who is rated at around £12.5million - can play on either wing or as a central striker, and is widely regarded as one of the brightest young prospects in South America.
Gazzetta dello Sport is now reporting that Blues owner Roman Abramovich has stepped up his attempts to bring Ocampos to Stamford Bridge, and in the absence of a permanent manager, will oversee the planned discussions.
However, Chelsea will face competition for the talented teenager's signature from Juventus and Paris Saint Germain, who have both been credited with an interest in securing the player's long-term future.
One factor that could hamper Chelsea's bid to land Ocampos is the youngster's third party ownership - an unnamed businessman that owns 25 per cent of the player's financial rights.
Abramovich would have to persuade both the agent and River Plate to sell for any deal to comply with FA regulations that are not present in either France or Italy.