It has been clear for months that Martel, on loan from Mainz last season, would not be available to Cologne this campaign, but sporting director Thomas Kessler has yet to identify a long-term alternative.
A move for former Cologne player Ellyes Skhiri now looks unlikely to materialise, while West Ham United's Edson Alvarez has been ruled out on cost grounds.
Interest in Khedira is not new - Cologne had previously been credited with interest in the 32-year-old as a potential Skhiri alternative - but contact between the two parties has only now been made. Khedira himself has long been open to the idea of leaving Union Berlin, though Cologne have yet to make contact with their Bundesliga rivals over the Tunisia international.
Khedira, the younger brother of World Cup winner Sami Khedira, fits the profile of the experienced holding midfielder Cologne have been seeking, having previously been linked with a move to Borussia Monchengladbach before that interest cooled earlier this year.
The Stuttgart-born midfielder has made 287 Bundesliga appearances across spells with Stuttgart, RB Leipzig, Augsburg and Union Berlin, and remains a regular starter for Union, where he is contracted until the summer of 2027.
He also represented Tunisia at this summer's World Cup, featuring in three matches before the team's exit at the group stage, and scored five goals in 29 Bundesliga appearances for Union last season - his most productive campaign in front of goal to date.