Singh, the then general secretary of Samajwadi Party, is accused of sending bribe money to win over three BJP lawmakers during the 2008 trust vote.
His appearance before the police comes after the Delhi police issued summons to him under Section 160 of the Criminal Procedure Code, asking him to present himself before the Crime branch.
The decision to call Singh for questioning comes after the arrest of Suhail Hindustani, who allegedly acted as a liaison between Singh and BJP MPs.
On Sunday, police had arrested Sanjeev Saxena, once considered close to Singh who allegedly delivered cash to the MPs to vote in favour of the UPA during the trust vote.
The arrests and fresh investigations into the case have come after Delhi police was slammed by the Supreme Court last week for its "callous" approach in this case.
Besides Amar Singh, police is also expected to question Samajwadi Party MP Reoti Raman Singh and BJP MP Ashok Argal.
Questioning of BJP leader L K Advani`s former aide Sudheendra Kulkarni, who allegedly was behind sting operation to trap the bribe-givers, is also likely to take place.