Le Monde newspaper reported on Friday that Diack told French police he asked Valentin Balakhnichev, then-president of the Russian track and field federation, for 1.5 million euros (1.07 million pounds) to finance political opposition in Senegal in 2011.
Diack has been placed under formal investigation in France on suspicion of corruption and money laundering following a complaint from the World Anti-Doping Agency (WADA) last month, allegations his family called "excessive and insignificant".
Le Monde quoted from what it said were transcripts of Diack's interview with the police and an investigating magistrate in November, when he was questioned on suspicion of covering up positive dope tests on Russian athletes.
Sall, 50, was the main challenger to Senegal's then-president Abdoulaye Wade, 85, in the March 2012 election that was widely praised as fair and democratic.
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"President Lamine Diack affirms that he never gave the slightest sum of money to the candidate, Macky Sall, who became president of Senegal, nor to his electoral campaign managers," Diack's lawyers Daouda Diop, Christian Charriere-Bournazel and Alexandre Varaut wrote in the statement emailed to Reuters.
"Everything, both in his declarations to the police and to the investigating magistrate, demonstrates this," they wrote. "Any contribution that may have come from Russia to Senegal has no link with either the functions or the actions of Mr Lamine Diack in his role of IAAF president."
"He reaffirms finally that he neither sought nor obtained personal enrichment."
Reuters' calls to Balakhnichev on Friday evening were not answered, but Le Monde quoted him as denying having had such a discussion with Diack or being involved in such an arrangement.
Diack, who has been released on bail but is banned from leaving France, was quoted as telling investigators: "At that time, there were the suspension problems of the Russian athletes a few months ahead of the world championships in Russia.
"We came to an agreement, Russian-financed. It's Balakhnichev who organised all that."
Last month, Russia was suspended from international athletics on the recommendation of an independent WADA commission, which had uncovered systematic state-sponsored doping and cover-ups.
Balakhnichev, who stepped down as head of the Russian athletics federation in February, has denied WADA allegations of conspiring to blackmail athletes ahead of the 2012 London Olympics. He has also said he will take legal action to defend his name and that of Russian athletics.
(Reporting by James Regan and Julien Pretot; Editing by Tom Heneghan)
