Lineker used the BBC‘s pre-game coverage of the Italy-Albania Euros clash to air an emotional tribute after Hansen, a Liverpool and Scotland legend, fell unexpectedly unwell.
It was on Monday revealed that Hansen, 69, was hospitalised in news leaving the football world shocked and saddened.
Hansen appeared 614 times for Liverpool in an illustrious career that delivered eight top-flight titles.
He then went into broadcasting as a BBC Match of the Day co-host.
Former colleague Lineker said it had been “a tough week for everyone associated with Match of the Day”.
He said: “The news that Alan Hansen is seriously ill in hospital shocked us all.”
Broadcasting alongside Lineker was former Newcastle striker Alan Shearer, who added: “We’re great friends with Alan, we know his character, we know he’s a fighter, we know how tough he is.
“We’re thinking of you big man and we’re with you. We’re hoping, we’re praying for you.”
Lineker added: “Everyone at Match of the Day sends love and thoughts to Janet, Lucy, Adam and the grandchildren.
“To use an analogy from Alan’s favourite past-time golf, you might be three down with four to play, but if anyone can come back from it, it’s Alan.
“I’ve never known a more competitive person in my life. We’re all with you Big Al.”
The emotional message came after fellow former Scottish footballer Graeme Souness spoke about Hansen ahead of the Scotland-Germany tournament opener.
Speaking on ITV, Souness said: “I believe he was the best footballing centre-half ever. And I know that is some statement but I really believe that.
“I saw it first hand he was a really quality performer and a great human being.
“You know when people are in trouble with illness, people say they’re great guys, but I’m telling you he is a great guy.
“You’d have to search a very long way to find anyone saying a bad word about him – that takes some doing.”
Souness added his old teammate and friend was “in the fight of his life right now”.
The pair played together at Liverpool from 1978-1984, claiming multiple cups alongside each other, and for Scotland from 1979-1987.
Souness said: “We should all say a little prayer for him.
“I had the pleasure of playing with him, he was an absolute dream.
“He passed the ball at the right weight, at the right angle, at the right time.”
Liverpool put out a statement on its website saying every member of the club had Hansen in their thoughts.
It said: “The thoughts and support of everyone at Liverpool FC are with our legendary former captain Alan Hansen, who is currently seriously ill in hospital.
“A defender of the utmost elegance, Hansen’s outstanding raft of honours across a 14-year spell with the Reds – he joined from Partick Thistle in 1977 – included eight league titles, three European Cups, two FA Cups and three League Cups.
“The club is currently in contact with Alan’s family to provide our support at this difficult time, and our thoughts, wishes and hopes are with Alan and all of the Hansen family.”
Nicknamed “Jockey”, Hansen is 10th on Liverpool’s all-time game appearances list. He was the club’s captain for four seasons.
ICONIC RANT
By Joshua Jones
ALAN HANSEN won it all in his glittering Liverpool career.
His stunning trophy cabinet included EIGHT league titles, three European Cups, four League Cups and two FA Cups.
And yet it is his iconic rant as a pundit on Match of the Day that a whole generation of football fans will know him for best.
Manchester United had been beaten 3-1 by Aston Villa on the opening day of the 1995-96 season following a summer of turnover.
Out had gone Paul Ince, Mark Hughes, and Andrei Kanchelskis and into the starting XI came youngsters such as Paul Scholes, David Beckham, Nicky Butt and Gary Neville.
Hansen was clearly unconvinced by the distinct lack of experience in the Ferguson team and boldly declared in his thick, iconic Scottish accent after that Villa loss: “You can’t win anything with kids.”
Fast forward to the end of the season and he was left with egg on his face as United wrapped up a league and cup double.
But it was short-term pain, long-term gain for Hansen who never shook off the phrase and openly admitted it was what “made him” as a pundit.