The American WorldTour team will meet with Contador's agent, his brother Francisco, soon to determine if an agreement can be made. Contador races for team Tinkoff, which is due to close its doors at year end after owner Oleg Tinkov pulled his sponsorship money.
"We are on the market for a Grand Tour classification rider and we want to see what's possible with Alberto, especially after he announced that he wants to continue for another two years," Trek-Segafredo General Manager Luca Guercilena told Cycling Weekly.
"We are far off from an agreement at this point. Talks are in the early days. Clearly we are going to set down with his brother and see what's possible. Anyway, it would not be until August 1 because of the UCI’s rules until we can say or announce anything even if Tinkoff closes shop."
Contador is one of only two active cyclists with Vincenzo Nibali (Astana) with wins in all three Grand Tours and only one of six in the history of cycling.
The 33-year-old from the outskirts of Madrid won the 2008 and 2015 Giro d'Italia, the 2007 and 2009 Tour de France, and the 2008, 2012 and 2014 Vuelta a España. After trying for the Giro/Tour double last year, he is aiming for a third Tour title this July.
Watch - Pro bikes of 2016: Bauke Mollema
"He's interesting for us," Guercilena added. "Clearly, he knows our sponsors and team. He should know that if he wants a calm and stable environment than this is the place."
Tinkov criticised Contador via Twitter after he under-performed in the 2013 Tour de France. Guercilena laughed off the idea that he would take to social media and complain about his own cyclists.
The Italian manager already tried to sign Nibali, but that deal fell through with the star likely riding for the new Bahrain team in 2017. Working in the team's favour, Contador already rode on Trek bikes in his years with Discovery Channel and Astana when he won his two Tour titles.
"So he knows the bikes and the company," Guercilena said. "I hope that this is an advantage but for sure, that's not enough on its own."
The team is busy in these months as it only has four to five cyclists on contract for 2017. 2012 Giro victor, Canadian Ryder Hesjedal will likely not continue as he could retire. Classification cyclist Bauke Mollema may renew.
Cycling Weekly learned from an insider that Trek-Segafredo already signed John Degenkolb for 2017. The German currently with team Giant-Alpecin won the 2015 Milan-San Remo and Paris-Roubaix, but suffered this year due to a training crash with a car.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1