The Reds are in the market for another proven performer in that area of the field.
Alberto Moreno departed Anfield at the end of the 2018-19 campaign when his contract came to an end, and has since linked up with Villarreal.
Jurgen Klopp now has no senior alternative to Robertson on the left side of his defensive unit.
A number of potential targets have been mooted for the Reds, with a quiet window having been taken in so far.
The former defender believes Klopp should be plotting a move for Sessegnon, with the highly-rated 19-year-old having suffered relegation out of the Premier League with Fulham last season.
“Still a teenager,” Nicol, a man who tasted First Division title and European Cup success with the Reds told ESPN FC.
“Well he [wouldn’t be] starting, he’s pushing.
“He’s there to push and he’s there to make the 11 that start better.
“He’s still a teenager, still has a lot to learn.
“But, what, in two or three years time, he’s pushing Robertson or anybody else down that left-hand side.”
Sessegnon’s current contract at Craven Cottage is due to expire in the summer of 2020.
It has been suggested that he may look to run that deal down before making a decision on his future.
Fulham, though, could be tempted into a sale if a suitable bid is lodged at this stage, rather than run the risk of seeing a price set by a tribunal once Sessegnon becomes a free agent.
Liverpool would be getting a player of considerable potential were they to make a move, with an England U21 international having enjoyed a meteoric rise to prominence over recent years.
He did not make the impact expected of him in the Premier League last season, but that was partly due to the struggles endured by Fulham as they slipped into the second tier after just one year back among the elite.