The German international is on trial with the SPL champions after being released by La Liga outfit Real Betis after a series of knee injuries hit his game time.
Gers boss Ally McCoist is running the rule over the 27-year-old winger, who came to prominence at Borussia Dortmund before earning a £5.25m move to Betis in 2006.
Odonkor broke into the Germany national team in 2006 and made four substitute appearances in the World Cup finals. Albertz said: "The key with David is whether he is fully fit.
"When he played with Dortmund he had blistering pace and was a player who could take defenders on and beat them.
"He has had problems with knee injuries and the fact that his contract has expired at Betis and they have let him go means that Ally will have to look very carefully at his fitness. But he is someone who would definitely give them an extra option going forward.
"He is still just 27 and will feel he has a few good seasons left. If he can land a deal at Rangers and hopefully get back into the Champions League, he can resurrect his international career.
"So this trial period will be very important to Odonkor. It will be very interesting to see how it works out."