Kumar received telephonic calls from Singh and Mukherjee but he told them that he will discuss the issue with party leaders, sources close to him said.
JD-U is a key constituent of the BJP-led NDA which will be meeting here tomorrow to firm up its stand on the Presidential poll issue, particularly in the wake of UPA nominating the Finance Minister for the top job.
JD(U) has 21 Lok Sabha MPs, nine members in Rajya Sabha and 118 MLAs in Bihar Assembly.
NDA is in a dilemma as to whether to field any candidate against Mukherjee or support P A Sangma, whose candidature has been proposed by AIADMK and BJD.
Trinamool Congress is pushing the candidature of former President A P J Abdul Kalam but JD(U) seems reluctant to back him and is understood to have made it known at the NDA meeting held here yesterday.
JD(U) national spokesman Shivanand today said he would like a "graceful send off" to be given to Mukherjee who is anyway on the verge of retirement, suggesting his inclination for supporting the veteran Congress leader for Presidentship.
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Sources close to Kumar insisted that no discussion has taken place in the party on Mukherjee's candidature.
Tiwari, who is in Patna and will attend the NDA meet tomorrow along with party chief and NDA Convener Sharad Yadav, said he was not aware of Mukherjee making a telephonic call to Kumar.