The 31-year-old reportedly came close to joining Tottenham in January after they agreed a £5 million fee with Liverpool.
Liverpool decided to pull out of the deal at the last minute, however, and Robertson remained at the club with his contract set to expire at the end of the season.
Speaking after their 3-1 FA Cup win over Wolves on Friday (March 6), Robertson revealed it was his decision to call the deal off.
"There was obviously interest there - there were discussions had with both sets of clubs," he said.
"But the decision was that I wanted to stay. We stayed at Liverpool and that was the decision made. I was never not committed.
“I've been committed to Liverpool for the last eight and a half or nine years now and I'll be committed until I'm no longer needed. That's always been my mindset.
“This club has given me everything and I've given this club everything."