The Reds side sit top of the Premier League with five games remaining and face a crucial game with third-placed Manchester City on Sunday.
Former Republic of Ireland midfielder Whelan captained Liverpool to their last league title in 1990, and speaking to Geoff Shreeves on Weekend Warm-Up, he urged the current crop to seize this opportunity.
"I think this is the best chance Liverpool will have for a long time," said Whelan, who won six league titles during his time at Anfield.
"They've already qualified for the Champions League - that's pretty much a given - but that means they're looking at a lot more games next season.
"They don't have the squad to take them through the Premier League, Champions League, FA Cup and League Cup. They will need to add more players, but it's going to get much harder to win the Premier League after this season."
Whelan has been impressed by the form of Steven Gerrard this season. The Reds skipper is playing a deeper midfield role and appears to be revelling in it.
"Steven is now playing in front of the back four, rather than running wherever he wanted to run," said Whelan.
"That was in his DNA, he always wanted to get forward. Now he knows the job. You sit in there, cover for your full-backs if they go forward or if your centre-back steps out of the line, and I think he's done that brilliantly."
Every game in England this weekend kicks off seven minutes late as football remembers the 25th anniversary of the Hillsborough Tragedy.
Whelan was captain of the Liverpool team that lined up against Nottingham Forest for the FA Cup semi-final on that fateful day, and he hopes that those who lost loved ones will soon see justice.
"The emotions are still extremely raw, and now that we're finding out more and more, it's getting a lot worse," he said.
"People have waited an awful long time for justice and have campaigned extremely hard."