However, a Manchester United approach is a much different proposition and with Pogba available to encourage Lemar into joining the Red Devils, it may just become much more of a possibility, with the player seemingly disinterested in joining Arsenal.
Some 14 years ago, back in the winter of 2003, a certain Wayne Rooney was readying himself for a run-out at Old Trafford.
Keane comes up against his former club on Sunday for the first time in Everton colors, and will hope to help his new side get a result against United at Old Trafford. In the box he's really unsafe, he's fast, he's strong. We have seven games in 21 days, that's not what we are used to from last year because the Champions League is in the middle and last year it wasn't there.
Koeman has rightly said that it is not the right time for shedding frustration, because they can hardly do anything before the next transfer window kicks in. There is no doubt Jose Mourinho's men will try to extend that positive run in front of their own crowd. No goals scored, eight conceded. Yes, he has pace but he's not physically the strongest.
"A striker is very important but last season we had a very good striker for two thirds of the season and that was not enough to win the title, so it's not just the striker".
The striker has hit five goals in his five games this season and even if he's unlikely to ever equal Rooney's heights, he's already on his way to making a massive impact.
Koeman claimed victories over Louis van Gaal's United in January 2015 and 2016 with Southampton, while only a last-gasp Zlatan Ibrahimovic penalty against Everton in April denied him a hat-trick of Old Trafford wins.
Mourinho went on to declare he was happy with the squad he has assembled at United and he believes the relationship between the club's supporters and their team has changed for the better.
But if there is one weakness in Man United it's their defence and new Everton signings Gylfi Sigurdsson and Sandro Ramirez will be the lead characters tasked with dismantling the home team's rearguard.