Singh spoke to Sidhu in the morning and assured him of looking into his grievances, sources close to the BJP president said.
The Amristar MP will meet Singh in the capital after the ongoing IPL cricket tournament gets over, they said.
Sidhu was not available for comments as he is busy with his commitments in the IPL season.
The cricketer-turned-politician has been sulking for quite some time and the matter precipitated after he was recently dropped from Singh's new list of BJP office-bearers.
He was Secretary in BJP during Nitin Gadkari's tenure as president.
Sidhu is also keen to change his constituency following his differences with top Akali leaders in the area, including Punjab Minister Bikramjit Singh Majithia.
Majithia, brother-in-law of Punjab Deputy Chief Minister Sukhbir Singh Badal, is the in-charge of Akali in the area.
Sidhu has won from the Amritsar Lok Sabha constituency thrice. His wife Navjot Kaur Sidhu won as an MLA from Amritsar in the 2012 Punjab Assembly elections.
Though Sidhu has remained silent, his wife, who is also a Parliamentary Secretary for Health in the state government, has made utterances about Sidhu not contesting the Amritsar seat again after being "ignored" by the party.
A section of BJP is of the view that Sidhu is neglecting his constituency and he is keen on moving out. "My husband will not contest parliamentary elections from Amritsar and a decision in this context was taken long back as the BJP ignored and sidelined him and his local team, which have been working in the constituency for more than a decade now," Kaur told PTI yesterday.
Kaur had stirred up a controversy within the BJP's state unit by commenting on a social networking site that her husband felt "sidelined and ignored" in the party.