The Uruguay international has struggled this season despite scoring a hat-trick in the El Clasico win over Real Madrid.
He returned from his post-World Cup holiday to accusations that he was overweight but has managed to score nine goals in 16 appearances in all competitions.
Suarez turns 32 in January and though he is contracted to the Catalan giants until 2021 his days at the Nou Camp look like they are numbered.
The former Liverpool favourite admitted at the start of November it was "normal" that Barca would begin searching for his replacement.
Their pursuit of Antoine Griezmann last summer became public, with the France international eventually opting to stay at Atletico Madrid.
But Griezmann is not among the group of players who are being considered by Barcelona on this occasion.
According to Sport, top of the wishlist is Ivory Coast international Pepe, who has netted eight goals and contributed seven assists for Lille in 14 appearances.
He scored in the recent 2-1 defeat to Paris Saint-Germain and has been linked with moves to Bayern Munich and Borussia Dortmund.
Arsenal are also said to be interested and the 23-year-old admits to being fond of all the sides keen on his services.
He said: “A preference between Dortmund, Bayern or Arsenal? They’re all big clubs.
“I was not aware of these rumours, although it’s nice.
“Will I leave Lille at the end of the season? We do not even know what I’ll be doing tomorrow.”
Barcelona were confirmed as a potential suitor earlier in the season but Lille president Gerard Lopez has stated several sides are monitoring the winger.
Genoa's Krzysztof Piatek and Benfica forward Luka Jovic – who is currently on loan at Eintracht Frankfurt – are said to be among the other forwards being considered by Ernesto Valverde's side.
But it appears inevitable that the club will invest in a new striker – leaving Suarez's future with the La Liga champions looking bleak.
Whether Arsenal do indeed firm up their interest in Pepe or not, it promises to be a busy January transfer window for the Gunners.
Roma ace Cengiz Under is among their targets for the winter, with club officials having been to watch the Turkey international.
SunSport understand players could also leave The Emirates Stadium in early 2019, with manager Unai Emery wanting to offload Mohamed Elneny for a fee of around £15m.
Leicester City are interested in the Egyptian, who has played just four times this season.
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