The 20-year-old was linked to several other Championship sides this transfer window, but it looks like Swansea will have the final word.
Following loan spells at Sheffield United and Ipswich Town last season, there was talk that he would most likely move to one of those sides.
However, Swansea came out on top, as boss Graham Potter is looking to bolster his defensive options.
Defenders Alfie Mawson, Federico Fernandez, Kyle Bartley and Jordi Amat were all sold during the summer transfer window.
The loan window for the EFL closes on August 31.
Carter-Vickers, who has won four caps for the United States, signed a new deal with Tottenham in May, tying him to the club until 2021.
Swansea have had the dream start to the season, going unbeaten under new manager Potter and moving up to sixth in the table.