But rejecting that claim Abdullah told reporters that if it were true Anwar "would have announced it by now".
Referring to a "game of political lies" he said speculations over the future of his government were a "waste of time".
Nonetheless he did not rule out a meeting with Anwar "if there is anything concrete to discuss at a suitable time".
"Do you think [Anwar] would ask for a meeting with me to discuss a transition?" he said. "He would storm into my room with hundreds behind him, shouting victory. This is Anwar's style."
Abdullah also said that he did not feel compelled to quit despite repeated calls for his resignation after the ruling Barisan Nasional (BN) coalition suffered unprecedented losses in March general elections.
|Anwar said he will ask Abdullah for a smooth transition of power [EPA]
On Monday night Anwar, a former deputy prime minister, told thousands of supporters at a rally outside Kuala Lumpur that he was seeking a meeting with Abdullah with the list of names of defecting MPs.
He said he wanted to discuss a smooth handover, and called for an assurance that the government would not deploy police and military onto the streets to remain in power.
Anwar's opposition alliance currently has 82 seats in the 222-member parliament, and needs the defection of at least 30 government MPs to form a government.
"We do not want to force it," Anwar told Monday's rally. "Therefore, we want to negotiate with the prime minister and ask him, 'Do you want one week, do you want two weeks?'"
The opposition alliance organised the rally to mark Malaysia Day, when Sabah, Sarawak and Singapore joined with the states of the Malayan peninsula to form the Federation of Malaysia in 1963. Singapore withdrew two years later.
The rally comes amid escalating political tensions in Malaysia, with Abdullah facing mounting pressure to stand down.
On Monday a cabinet minister resigned over the arrest of three people last week under the colonial-era Internal Security Act (ISA), which allows for indefinite detention without trial.
Zaid Ibrahim, the outspoken de factor law minister, criticised the use of the ISA on civilians and offered to resign over his views that he said will be at odds with Abdullah's cabinet.
Abdullah however rejected the letter and told Zaid on the same day to take two weeks leave and reconsider his decision. But on Tuesday Zaid was quoted in The Star, a leading English daily, as saying that he was sticking to his decision.
An opposition MP, a journalist from a local Chinese-language newspaper and a prominent blogger were all arrested on Friday for allegedly stoking racial tensions.
The arrests were widely criticised by lawyers, human rights groups and some half a dozen government ministers.
The reporter with a Chinese-language newspaper was freed Saturday but the other two remain in jail.
Anwar has recently faced charges of sodomising a male aide similar to those which saw him sacked from the government in 1997 and subsequently jailed.
His conviction for sodomy was later overturned, although a conviction on a separate corruption charge still stands.