Last summer Sporting sold Viktor Gyökeres, 27, to Arsenal and replaced him with Suárez, 28, who joined from
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Spain's UD Almería.
The Colombia international has impressed, scoring 31 goals and providing five assists in 39 competitive matches.
According to journalist Sébastien Vidal, Newcastle are now showing interest in Suárez.
The Toon are said to be working on the signing, with a price-tag mentioned of €50m.
Suárez is under contract with Sporting until the summer of 2030.