After signing with Washington, the safety would love to keep wearing the number if the team and family approve.
It "would be an honor ... if the family would allow me to," he said.
"I hope, I hope, that's big shoes to fill," Collins added about the possibility of wearing No. 21, via the Washington Post.
No Washington player has worn No. 21 since Taylor was killed.
Redskins owner Dan Snyder presented Collins with a signed Taylor jersey Wednesday night after the safety signed in Washington. Collins said he broke down after being given the gift.
"I couldn't say nothing, I couldn't touch the box," he told The Team 980 radio. "My son was in my lap, he's just opening the box, and he pulled out the jersey and I broke down. It was breathtaking. I think I was sitting there for 20-30 minutes. I couldn't eat, just staring at the jersey there in the box. It was an honor. I thank Mr. Snyder for that. He's going to get the same passionate kid that he had in Sean Taylor in me, I promise you that."
The team has not yet announced numbers for its free agent acquisitions.