Tiger Woods and Lindsey Vonn
Mick Tsikas/Reuters/Landov; Luis Guerra/Ramey
02/09/2013 at 08:00 PM EST
It was quite the gesture.
After Lindsey Vonn
suffered a devastating injury
during the Alpine World Championships in Austria, she got a bit of help from Tiger Woods
. Walking on crutches, Vonn – who tore two ligaments in her right knee and fractured her shin when she crashed on Tuesday – boarded Woods's private jet to return home.
Is it a sign that the rumored relationship
between Woods and Vonn is heating up?
"Tiger and Lindsey have been friends for a while, and nothing started out romantically at all," a source tells PEOPLE. "But they really have a lot in common and got closer and closer. He still refers to her as 'my very good friend,' but he's been spending more and more time talking to her – and talking about her."
Last month, Vonn's reps kept mum about the rumored relationship, telling PEOPLE that her "focus is solely on competing and on defending her titles and thus she will not participate in any speculation surrounding her personal life at this time."
But the source close to Woods tells PEOPLE that Woods, 37, and Vonn. 28, talk and text frequently.
"Tiger really does want a woman who he can have good conversations with," he says. "He wants shared interests and outlooks. He is finding that with [Lindsey]."
Woods made international headlines in 2009 when he was linked to dozens of women while still married to his ex-wife
, Elin Nordegren
Since then, he has dated sporadically, but struggled to find someone who wanted a relationship for the right reasons.
"She's not freaked out by his past, and that's really appealing to him," says the source. "He really does deserve to be happy. He has been flogging himself for three years, and it's good to see him moving forward."