The threat of legal action was reported in Dutch newspaper Het Financielle Dagblad and comes after Amro has been in exclusive negotiations with Barclays with a view to the two banks merging.
TCI, which currently holds a one per cent stake in Amro, had earlier been agitating for the underperforming Dutch bank to break up its assets to better serve its shareholders.
Should TCI pursue the matter, it is likely that it would request an investigation from a Dutch Enterprise Court into formulation of policy at Amro and to look at why other bids were not considered.
It is thought that a raft of other banks are interested in either takeover bids or in buying parts of Amro, including Citigroup, BNP Paribas, ING, Santander and Royal Bank of Scotland.
Barclays and Amro last week announced that initial negotiations had seen the companies agree that the prospective new firm's headquarters would be located in Amsterdam.