Asked if the MPs were thinking of defecting, Mr Farron said he did not want to "betray confidences".
But he told BBC News it would be "not surprising" if they had serious doubts about the direction Labour was taking under Jeremy Corbyn's leadership.
Mr Farron said he was contacted via text messages after Mr Corbyn was elected Labour leader on Saturday.
He said he had also spoken on the telephone to Labour MPs, but he declined to name names or say whether they were front bench figures.
Speaking to the Evening Standard, he said: "I've had various unsolicited texts, some of them over the weekend, where I felt like I was being an agony aunt rather than anything else.
"People who have been members of the [Labour] party for as long as I've been a member of mine who feel that they don't recognise their party anymore and feel deeply distressed."
Mr Farron, who was elected Lib Dem leader in July, was speaking ahead of the party's annual conference in Bournemouth, which gets under way at the weekend.
It is the party's first gathering since its crushing defeat at May's general election, when it lost all but eight of its MPs.
Mr Farron has called the election of Mr Corbyn a "quite staggering opportunity" for his party to occupy the centre ground in British politics, which he believes is being rapidly vacated by the New Labour leader in favour of a hard left agenda.
Quizzed about his contacts with Labour MPs on the BBC's Look North, he said: "I am keen to be a decent sort and not betray any confidences - but it would be not surprising if Labour MPs, voters, members and indeed donors were thinking hang about this isn't the Labour Party that I voted for, I need a party that will hold the Tories to account, that can beat the Tories and which believes not just in social justice and fairness, but also in sound economics.
"Because you can't protect the health service if the economy goes down the plughole."
Former foreign secretary Jack Straw played down the prospect of Labour MPs defecting to other parties, suggesting the experience of the SDP in the 1980s made that "very unlikely".
But he said the new leadership could have a "Lazarus effect" on the Liberal Democrats, in an interview with BBC Radio 4's The World at One.
Lib Dem leader Tim Farron has been contacted by Labour MPs unhappy with their new leader, he has said.