Both clubs are understood to be showing interest in the 19-year-old centre-back, with several other unnamed clubs also said to be monitoring his situation heading into the closing weeks of the transfer window.
Coulibaly recently changed representation, a move widely read as an attempt to push through a transfer this summer. Fees as high as €45 million were discussed for the left-footed defender earlier in the window, though Werder Bremen are now understood to be willing to accept closer to €30 million.
The Bundesliga club would reinvest a large portion of any sale directly into fresh recruitment, giving Bremen an incentive to move quickly on a deal. That said, concrete interest from either Lisbon or Nottingham has not yet translated into anything firm.
An update from Sky reported that Racing Strasbourg have also been working on a possible agreement with Coulibaly. Werder are said to have already rejected two offers from the French club, with a third expected imminently.
Coulibaly progressed through Hamburger SV's academy before moving to Bremen's youth setup, signing his first professional contract with Werder in July of last year and making his Bundesliga debut only weeks later.
His rapid rise last season, in which he made 27 appearances as Bremen finished 15th, has made him one of the more sought-after young defenders in German football, with Chelsea, Paris Saint-Germain and Newcastle United among the other clubs previously credited with interest.
Bremen's asking price has come down steadily over the course of the summer, having started closer to €40 million before settling at the current level.
Sporting director Clemens Fritz has praised Coulibaly's development publicly on several occasions, and the versatile defender — who can also operate in defensive midfield or at left-back — remains part of head coach Daniel Thioune's plans for the new campaign for as long as he stays at the club.