Taylor broke and dislocated his ankle in a challenge with Sunderland's Craig Gardner but despite being expected to miss the rest of the season, the 24-year-old expressed belief he could return before the summer.
And after playing 80 minutes for Swansea's U21 side this week, Laudrup is hopeful the left-back can feature for the Swans, who have seven games remaining.
"Physically he is quite close to being back," said Laudrup.
"He has trained with us for some weeks, but we all know match fitness is a different level and only by coming back will he get that.
"The physical part is one thing, the mental part is another after a triple fracture, which is quite an injury.
"I am happy he's back and let's see when he can come in and make his comeback."
Laudrup has also been boosted by the fitness of Chico Flores and Angel Rangel who have returned to training ahead of Swansea's clash with the Canaries this weekend.
Kemy Agustien is also closing in on a return from a thigh injury.