West Ham's loss to Leicester at the London Stadium before the global break saw Sullivan apologise to fans on behalf of Bilic and the squad afterwards.
On the speculation, Bilic said: 'It does not annoy me. But Sakho has displayed a remarkable level of rehabilitation, and is realistically in with a shot to play for the Hammers next Wednesday versus Arsenal, or three days later against Swansea City.
Bilic would not be drawn into a discussion about his future, saying: "Even in that good period, when reporters were talking about a new contract, I said we were not finished and there were a lot of games to play".
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West Ham, 12th in the table, will hope to end a three-game winless run when they travel to face 18th-placed Hull. "But my head is clear and I am totally motivated and focused", said the Croatian.
The Hammers secured an impressive seventh-place finish in the Premier League in 2015-16 - Bilic's debut season at the helm.
West Ham owners David Gold and David Sullivan are renowned for making public their views - but Bilic is adamant he is not feeling any boardroom pressure. I am not bothered about that just yet [new contract]..
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He added: "I have a good relationship with both of them". I was telling you the same last season and earlier this season when you were talking about a new contract. We have a direct line and we talk. "I have a game on Saturday". We are able to climb up several spots if we win matches, we are able to go several spots down if we don't win matches.
Bilic is due to have captain Mark Noble, who has recovered from injury, back against Hull.
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