Castillo, 23, traveled to Ukraine on Monday. Greek media reported that Shakhtar had offered €16 million (US$21.8 million) to break Castillo's contract with Greek champion Olympiakos which ends in 2010.
The reports said Castillo was due to sign a four-year contract with an annual salary of over €2 million (US$2.7 million).
Olympiakos has not made any comment on the reports.
Castillo scored four goals to help his country finish third in the Copa America which ended earlier this month. Brazil won the tournament held in Venezuela.
After returning to Greece, Castillo said he had failed to successfully re-negotiate his contract with Olympiakos, where he has played for seven years.
"It was my wish to stay at Olympiakos ... but I did not hear what I expected to hear from them," Castillo said last week, confirming transfer interest from Shakhtar and England's Manchester City.
Castillo helped Olympiakos clinch its 10th league title in 11 seasons, scoring 12 goals.
Source: FOX Sports