Tymoshenko, who is prime minister, and opposition leader Viktor Yanukovich are both wooing Tigipko, who came a strong third with 13% of the vote in a first round on 17 January.
But she is keen for him to agree to work with her before the 7 February run-off as this would help lure voters who backed Tigipko, a 49-year old former central banker, in the first round.
"I am hoping he will give a clear answer so that people can decide on voting day in the second round of the elections," Tymoshenko told journalists.
Tymoshenko came in 10 percentage points behind Yanukovich in the first round.
She is expected to pick up many floating votes from other eliminated candidates, particularly in the Ukrainian-speaking west and centre. But she wants to win the support of voters in the Russian-speaking industrial east who backed Tigipko.
Analysts see a close contest between Yanukovich, 59, who lost the presidency in 2004 to President Viktor Yushchenko when his rigged election was overturned, and Tymoshenko, who is a strong public performer.
One of Europe's largest online bookmakers, bwin, was taking bets on the election, giving Yanukovich odds of 1.33-1 and Tymoshenko 3-1, according to its Web site. The publication of opinion polls is banned in Ukraine two weeks before a vote.
Unpopular measures
Tigipko has refused to back either candidate before the poll. On Tuesday, he said he was prepared to serve as prime minister under either candidate, but only if his conditions for taking "unpopular measures" to revive the economy were brought out in the open.
"Simply being handed a job does not interest me," he said in a statement. "I will not sign up to any back-room deals."
In an interview with Reuters on Monday he spoke of the need for painful reforms to modernise the economy and a tough budget to bring back International Monetary Fund support.
The IMF suspended its $16.4 billion bail-out programme to the ex-Soviet republic last year after parliament raised the minimum wage in violation of promises to control the budget.
Yushchenko has refused to back Tymoshenko's policy programme and Tigipko appears keen to avoid suffering the same fate in a new government.
Tymoshenko stressed on Tuesday that her election programme was similar to that of Tigipko, especially in the area of the economy - both speak of modernisation and a stronger social safety net. But Yanukovich also claims his plan of action is identical.
(EurActiv with Reuters.)
