The Swedish diplomat saved thousands of Hungarian Jews from Nazi gas chambers at the end of World War II. He has been missing ever since his arrest by Soviet forces in 1945.
Wallenberg's niece Louise von Dardel is travelling to Brussels where Putin is attending an EU-Russia summit on Tuesday in hopes of appealing directly for access to key documents about her uncle's death.
Soviet and Russian officials have argued that Wallenberg died of heart failure in Soviet custody in 1947 but never produced conclusive proof.
In the latest bid to achieve closure over his fate, Von Dardel, a 63-year-old who lives in Geneva, hopes to deliver a letter to Putin that asks to end the family's 70-year-long ordeal.
But Putin's spokesman Dmitry Peskov told Interfax news agency that a personal meeting was impossible.
"The president's schedule in Brussels has long been completed and is so tight that unfortunately it is physically impossible to find the time for any other meetings," said Peskov.
Historians have tried to unravel Wallenberg's fate for decades but concede that there is still no clear evidence that he died a natural death.
Historians from Russia's Memorial, a rights organization that works extensively with Soviet archives and has pursued Wallenberg's case, have said that there is a high likelihood that the Swedish diplomat was killed in a Soviet prison.
It has called on the authorities to make relevant classified documents available.
Russian rights ombudsman Vladimir Lukin on Monday said that there was little reason to keep the files locked as the people involved in Wallenberg's death must certainly have passed away.
"If we have even the smallest details that have not been made public, they must be made public," Lukin told Interfax.
"Decades have passed. People who had anything to do with this story have likely died. It's a historical issue, and it must be 105 percent clear," he said.