Collins, who signed a reported six-year, $84-million contract as a free agent, wore No. 21 with the New York Giants. The safety said he'd love to continue wearing the number if the team and Taylor's family approve.
"It would be an honor if the family would allow me to (wear No. 21)," Collins said, according NFL.com's Kevin Patra. "I hope, I hope, that's big shoes to fill."
Taylor was killed in November 2007 at just 24 years old. No Redskin has worn No. 21 since.
After officially signing with Washington, Collins was presented a signed Taylor jersey by team owner Dan Snyder.