Sir Elton, 68, posted a photograph of Putin on Instagram, with a caption that read: "Thank-you to President Vladimir Putin for reaching out and speaking via telephone with me today.
"I look to forward to meeting with you face-to-face to discuss LGBT equality in Russia."
Sir Elton did not reveal exactly what the pair discussed, or when they will meet.
However, Putin has denied that the phone call ever took place.
The Press Association reports that Putin's spokesman Dmitry Peskov told Russian news agencies that the president had not spoken with Sir Elton.
Mr Peskov said: "Putin did not have a conversation with Elton John, and, what's more, we have not received any requests from him for a meeting.
"The president has always been open to discuss human rights issues.
"The president, I'm sure, will be ready to meet with Elton John, too, if there is such a request."
The alleged phone call follows Sir Elton's visit to Ukraine, where he met President Petro Poroshenko to discuss the importance of legislative changes to support LGBT rights.
Sir Elton posted pictures of his visit to Ukraine on Instagram, where he thanked Poroshenko for his "support" after meeting with him.
He said he asked Poroshenko to ban discrimination in the workplace based on sexuality and gender identity and provide criminal penalties for hate crimes.
After visiting Russia's neighbour, the gay rights advocate said he wanted to meet with Putin to discuss the president's "ridiculous" attitude to equality.
Speaking to the BBC, Sir Elton said he would welcome talks with Putin even though "he may laugh behind my back... and call me an absolute idiot".
The musician also spoke out against comments Putin made last year in which he indicated that gay people target children.
Russian President Vladimir Putin denied calling Sir Elton John
Addressing the safety of homosexuals at the Winter Olympics last year, Putin said: "One can feel calm and at ease,” adding: "Just leave kids alone, please."
Sir Elton was unimpressed with the remarks, saying: "Give me a break. You are President of Russia, and you go and say stupid things like that?"
Russia has been placed under increased scrutiny over its treatment of homosexuals. A report by Human Rights Watch found that authorities had "failed" to prevent and prosecute homophobic violence.
Vladimir Putin is due to meet Sir Elton John "face-to-face" to discuss LGBT equality in Russia
Tanya Cooper, Russia researcher at HRW, said: “Violence experienced by LGBT people in Russia is unmistakably motivated by homophobia, but the authorities deliberately ignore that these are hate crimes and fail to protect victims.
“Russian authorities should effectively prosecute homophobic violence, and the authorities should stop engaging in and tolerating anti-LGBT discrimination.”
Vladimir Putin is said to have "reached out" to Sir Elton John after the singer criticised the president's "ridiculous" attitude to gay rights
HRW found that a growing number of lesbian, gay, bisexual and transgender (LGBT) people had been attacked and harassed across Russia in the lead-up and aftermath of the adoption of the federal anti-LGBT “propaganda” law in June 2013.
The law caused international outcry as it was widely perceived to effectively legalise discrimination against LGBT people.