According to Sky Germany, Werner will embark on a six-month loan deal until the end of the season, with Spurs covering the entire salary of the German.
Following a two-year stint at Chelsea, where he helped win a Champions League title but struggled to establish himself as a consistent goal scorer, he eventually returned to Leipzig in 2022.
Werner's rare Bundesliga appearances - only eight this season - might not qualify him for consideration by national coach Julian Nagelsmann for the European Championship squad.
"It's right that Timo is looking for a loan. Timo would like to go to the European Championships," Leipzig manager Marco Rose told Sky Germany.
"We wish him all the best and keep our fingers crossed for him."
Werner could provide cover for Spurs up front with the club's top scorer Son Heung-min away at the Asian Cup for South Korea.
Spurs are currently fifth in the table with 39 points, six behind leaders Liverpool.
