Gen (retd) Singh has not been able to provide documents to support his allegation and enquiry conducted by the CBI so far also does not conclude such a deal, official sources said.
The agency had registered a Preliminary Enquiry against unknown people to probe the matter but nothing has concrete has emerged from the investigation, they said.
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The CBI had also recorded statement of the former Army Chief in this regard and a decision to close the PE is likely to be taken soon, the sources said.
The bribe offer, according to Gen Singh, was made in 2010 and the former Army Chief was unable to explain why he had maintained a silence for more than two years, they said.
A PE is formal initiation of probe before registering an FIR but during this phase the agency does not have powers to question, search or arrest.
The CBI had on April 10, last year received a complaint from Gen Singh about the alleged bribery offer made to him by retired Lt Gen Tejinder Singh, who has denied the charge, terming it as absolutely false and concocted.
The former Army Chief had alleged that Tejinder Singh had offered him a bribe of Rs 14 crore, a matter he had reported to Defence Minister A K Antony, to clear purchase of nearly 600 all-terrain Tatra BEML trucks.
Tejinder Singh has also slapped a defamation case against the former Army Chief and other officers.
Gen V K Singh was asked to submit detailed description of the incident, list of possible witnesses and supporting documents on the issue but these were never received by the probe agency, they added.