The steel business was put up for sale on March 30, but has failed to attract the attention of most major British investment banks.
Bankers at only two of 10 major investment banks contacted by Reuters earlier this week said they were sounding out potential buyers. Five said they were not seeking any role and three said they had not made a decision.
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Standard Chartered declined to comment. Also, Tata Steel could not be immediately reached for a comment.
The news was first reported by Sky News.