The Daily Telegraph reports that Barclays, Royal Bank of Scotland and Citigroup are among the banks that have issued the orders, according to the Financial Times.
Communications between traders are believed to have been central to the alleged fixings of Libor, for which several banks face fines of hundreds of millions of pounds.
Logs of chats released following investigations appear to show traders asking others to set rates artificially low or high, in some cases offering gifts in exchange.
The banks have banned traders from visiting chat systems that multiple banks previously had access to, according to the report.
As well as probing Libor, regulators in the UK, Europe and the US are investigating allegations that banks rigged currency trades in order to make a profit.
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