The Gunners have been linked with a potential swoop to sign the England Under-21 international at the end of the campaign but face competition from a number of Premier League rivals.
Liverpool FC, Manchester United and Tottenham Hotspur have also been linked with a bid for the 17-year-old, who has proved fundamental in Fulham’s bid to secure promotion to the Premier League ahead of the 2018-19 campaign.
The promising full-back has scored 15 goals and has made six assists in 45 appearances in the Championship to help the Cottagers push for a return to the Premier League for the first time since 2013.
Former Arsenal defender Winterburn, who earned a reputation as one of the Premier League’s best left-back during his career, believes Sessegnon would be a good addition to the Gunners squad.
“I think he’s a fantastic player,” Winterburn told BetStars.
“I think Arsenal’s problem particularly over the last couple of seasons has been their inconsistency defensively and that’s why they’ve been knocked out of the Europa League over the two legs.
“It seems strange to say that Arsenal probably were the better team over two legs and we’re looking at two defensive errors that have cost them the chance of going through.
“They need to increase the quality but I do believe the structure defensively is going to have to change slightly than it is at the moment because we play far too open for the players we have in our squad.”
Arsenal haven’t won the Premier League title since 2003-04 when the Gunners had Ashley Cole playing at left-back in their unbeaten season.
The north London side lost 2-1 on aggregate to Spanish side Atletico Madrid in the Europa League semi-final.
Arsene Wenger is set to stand down as manager at the end of the current campaign following a difficult season.
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