On Friday the UK watchdog suggested that giving the contract to the pair may contravene antitrust rules.
The Competition and Markets Authority (CMA) said it was considering whether the First-Trenitalia joint venture could result in a situation that “may result in a substantial lessening of competition”.
To build its potential case, the CMA has invited industry organisations and interested parties to comment on the transaction.
When the Department for Transport awarded the franchise last month it stoked the long-rumbling debate about Britain's railways being run by foreign state-owned firms.
As well as running West Coast services out of London Euston from 8 December 2019 to 2026, DfT also announced that partnership will then run services on the new HS2 line through to March 2031.