The 29-year-old Ukrainian is said to be eager for a new challenge.
Malinovskyi would rather a move to Tottenham to work with Antonio Conte, according to Calciomercato.
But Spurs are only reported to be willing to bring the midfielder to the club on loan.
However, Atalanta will not consider a temporary deal.
That seemingly leaves West Ham in pole position to swoop for the 51-cap international.
French club Marseille are also said to be waiting in the “background” in case he becomes available to them.
Malinovskyi is under contract with Atalanta until 2025, and the Serie A side are also thought to be reluctant to sell.
The player himself is reportedly intent on a fresh start after three-and-a-half years in Italy.
Spurs were previously linked in the summer, while West Ham are looking at making January additions to try and fire them up the table.
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Tottenham’s reported willingness to only sign him on loan comes despite Conte’s pleas for transfers.
After the 2-0 home defeat to Aston Villa, the Italian claimed Spurs must sign two players worth up to £70million every season if they want to become title contenders.
Conte said: “I continue to repeat that last season we made a miracle.
“It happened, why? Because we played only one competition and we played with 12 or 13 players that didn’t have injuries in the last 15 games.
“We did a miracle, but I knew what the situation was and then I was very clear with the club (over what was needed) to become title contenders.
“I remember very well in the summer people talked about Tottenham as title contenders but it was a bit crazy to see this.
“To become title contenders, to become a team ready to fight to win something, you need to have a solid foundation, which means to have 14 or 15 strong players, with quality, and the other young players to develop.
“Every season, you can add two players – but two players priced £50m, £60m, £70m.
“In this way, it means you are signing important players who can improve the quality and the level of your team. But this is a process, guys.”