There are two seperate reports about rumours that the US will redeploy troops to Azerbaijan.

First, Eurasianet.org has this report:

News that the United States plans a massive redeployment of its armed forces has Azerbaijanis wondering whether their country will soon host US troops. Azerbaijani officials are coy on the base question, prompting some local political analysts to say Baku is trying to leverage the issue to achieve a breakthrough on the stalled talks on a Nagorno-Karabakh peace settlement.

Inevitably there is speculation that the US will back them against Russia in the Karabakh dispute.

Meanwhile Yeni Musavat from Baku explores the Karabakh angle in more detail.

The USA might help Azerbaijan gain back its Armenian-occupied lands in
return for stationing its troops in Nagornyy Karabakh, Azerbaijani
daily Yeni Musavat has said. This could provide excellent chances to
Washington, which aims to reduce Russia’s role in the region and is
about to launch its plans vis-a-vis Iran, since Nagornyy Karabakh
borders both on Iran and on Armenia which hosts Russian military
bases, the report said. I do not believe that US troops will come here
only to protect the Baku-Ceyhan oil pipeline, the deputy chairman of
the opposition Musavat Party told Yeni Musavat. The US forces to be
deployed in the country will be “multipurpose”, the party official
said. For his part, the spokesman of the Azerbaijani Defence Ministry
denied that deployment of US troop had been discussed during the
latest visit by the US defence secretary to Baku. However, the
spokesman said, military units of countries involved in the
construction of Baku-Ceyhan might take part in the protection of the
pipeline. The following is an excerpt from Elsad Pasasoy’s report by
Yeni Musavat on 23 August headlined “US bases in Karabakh” and
subheaded “Can Baku make such an appeal to the USA?” and “Sulhaddin
Akbar: Personal and power interests should be set aside”; subheadings
have been inserted editorially:

Iran has threatened in the past to attack Azerbaijan preemptively if it allows foreign troops (read the US) to be stationed on its soil, which it sees as a provocation.