The American team sponsored by the famous bike manufacturer and Italian coffee giant met with Nibali on Monday. The package: a two-year contract and an ambassador role beyond 2021.
It is more than the offer from Nibali's current team Bahrain-Merida, who so far have proposed one year and little beyond that.
"Trek made a good offer, I liked it a lot," Nibali's agent Johnny Carera told Cycling Weekly.
"What can I say? We were also close to them three years ago before joining Bahrain-Merida. The fact that the heads were there make it easy for the team to continue beyond 2020, it's the entire package with Vincenzo."
Trek-Segafredo general manager Luca Guercilena and Segafredo's representative Luca Baraldi met with Nibali and Carera on Monday at the Milan Malpensa airport.
The team currently has deals with sponsors through 2020, but everyone is ready to continue and hoping to do so with Nibali on board. The team currently has Australian stage racer Richie Porte, who they signed in the off-season from BMC Racing.
Nibali has won all three Grand Tours, Il Lombardia twice and Milan-San Remo last spring. At 34, he wants to continue through the 2020 Olympics and World Championships and the 2021 season at a high level.
He helped kick-start the Bahrain-Merida team for the 2017 season after a chance ride with Bahrain's Prince Nasser Bin Hamad Al Khalifa. Following negotiations in 2016 with Trek-Segafredo and his then team Astana, he decided on a three-year deal with the new Middle Eastern team.
On Monday evening, Nibali and Carera met with Bahrain-Merida general manager Brent Copeland and managing director Milan Erzen to talk about a renewal contract. So far, they have only offered one-year. With British racing group McLaren now with a 50 per cent stake, more meetings need to happen before another offer will be extended.
"We heard their request of two years, we need to talk it over with McLaren and Sheikh Nasser," Copeland explained. "Then we are going to hopefully be able to make an offer for two years."
Copeland should extend an offer to his star rider by the end of January.
"We haven't discussed [a role after his racing career]. I know Trek-Segafredo is offering it. They can gain from it, a bike brand, and Segafredo is Italian," added Copeland.
"I don't see how a team that is sponsored by a consortium of sponsors in a country like Bahrain is going to benefit from that."
The ambassador role could be the decider for Nibali as he begins to look beyond 2021. It would mean changing teams at the end of 2019, riding new equipment and ensuring his staff follow, but it would offer him more security.
"It's not like one team is offering two million and the other 10 million euro, but it's that Trek-Segafredo is offering a future as an ambassador," Carera added. "We also have to consider the positive things in the team that we have now.
"The team started off with that [idea of an ambassador role], that was part of the reason we decided on Bahrain in 2017. Things changed, though, McLaren is in. They are going to have their say now, 50 per cent of the team, and the Prince too will have his say."
Nibali wants to wrap it up by the Giro's start, on May 11 in Bologna. He will race for a third title before going on to try to win the Tour again in July.
Another factor is Team Sky. If Nibali waits too long and David Brailsford fails to find a sponsor, both Bahrain and Trek could lose some interest with more star riders on the market.
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