Liverpool face Manchester City at Anfield on Sunday knowing a win would put them firmly in the driving seat towards their first Premier League crown.
Brendan Rodgers' side currently lead the table by two points from Chelsea, with City - who have two games in hand - a further two points adrift.
Whelan, who scored 46 goals in 362 appearances for the Reds between 1979-1994, said: "Nine games ago we wouldn't have said we would win nine games on the trot but now there are only five more to go.
"I know it will be a record, winning 14 in a row, but the team are playing well enough at the moment to do it."
Rodgers has overseen a huge change in fortunes for the club from their lowly seventh-placed finish last season.
Whelan believes Liverpool's irresistible form of late gives them the best chance of any of their rivals to claim their 19th league crown - their first since he was part of the team which last lifted the title back in 1990.
"You cannot fault anything they are doing, they are going out and winning game after game and doing it well," he said.
"The energy they are showing at the end of the season always gives you a chance in the last five games. The energy seems to be more than Chelsea and Manchester City and the other teams."
The Anfield legend was speaking ahead of the Celebration Of The 96 Charity Match due to take place on April 21 in aid of the Hillsborough Family Support Group and Liverpool FC Foundation.
Whelan will be representing the UK & Ireland team, managed by fellow Anfield great Kenny Dalglish, while the Rest of the World will be coached by former Liverpool boss Gerard Houllier.
"There is so much excitement among the players. To get all these players back together should be a great occasion," he added.
"It will get serious - Kenny always get serious. He'll be on the touchline shouting and I'll be thinking 'I'm 52 years of age, leave me alone!"