In a speech to a Washington think tank, the Liberal Democrat Treasury minister described the nuclear deterrent as "the UK's last, unreformed bastion of Cold War thinking".
David Cameron rejected the LibDem proposals before they were even published earlier this year. The Conservatives say they are committed to a "like for like" replacement of the aging weapons system on the Clyde.
The LibDems say it is wrong to spend billions replacing a system designed to "flatten Moscow".
The issue is expected to dominate Coalition negotiations in the event of a hung parliament after the 2015 general election.
A review into alternatives, helmed by Mr Alexander favoured an end to round the clock patrols. The report found the fleet could be operated with two or three boats instead of the current four.
In a speech to the Brookings Institution, Mr Alexander said: "There are some in the UK who argue that any change to our nuclear posture would cause serious disruption to our relationship, and not just as it relates to the Mutual Defence Agreement.
"But I believe the special relationship runs deeper than that. The Trident Alternatives Review is not a threat to our relationship; it is an opportunity to work together."