Valentin Balakhnichyov said the Olympic champion and world record holder had met Abramovich in Zurich in December when they were part of Russia's delegation bidding successfully to win the right to host the 2018 soccer World Cup.
"I know that Yelena had asked for help to fix an indoor arena in Volgograd," Balakhnichyov said on Monday.
"The problem is it gets quite cold inside the arena in the winter, making it very difficult to train. Also, the running track is quite old and needs to be replaced."
Abramovich's spokesman John Mann confirmed the report, telling Reuters: "Yes, it's true that Yelena has approached Roman for help and the talks are ongoing."
Isinbayeva's decision to return to Volgograd from her base in Italy should speed up the process, Balakhnichyov said.
"I was quite surprised how smoothly the talks have gone. I know that Abramovich had already asked his people to find out what has to be done and how much it would cost," he said.
"Hopefully, the work could be completed over the summer."
This month, Isinbayeva made headlines in Russia when she decided to leave coach Vitaly Petrov and return to her former mentor Yevgeny Trofimov following a series of poor performances in the last two years.
"Rebuilding the Volgograd arena should help not only Isinbayeva but all other athletes who train there," Balakhnichyov said.
"As you know in Volgograd we have not one but three Olympic champions in athletics: Isinbayeva, (long and triple jumper) Tatyana Lebedeva and (high jumper) Yelena Slesarenko.
"And we have many others who may follow in their footsteps," he said, adding that the sports ministry would share the cost.
"We also have athletes from the local youth sports academy who regularly train there, so (the) ministry will also get involved."
