Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
The Portuguese forward looked set to leave Upton Park on deadline day but a move failed to materialise, leaving him in limbo and boss Sam Allardyce with a player he would have been happy to get rid of.
But Allardyce handed Vaz Te a rare start in the Capital One Cup against Cardiff on Monday night and he responded with an all-action display culminating in the winning goal as the Hammers triumphed 3-2.
With attackers Andy Carroll, Joe Cole and Stewart Downing still injured, new signing Mladen Petric short of match fitness and Modibo Maiga struggling for form, Vaz Te is set to get the nod at Hull on Saturday.
Assistant manager Neil McDonald said: "He keeps on telling everyone that he creates chances and scores and that's what the manager wants - people to put the ball in the back of the net.
"That's a knock on the door for the manager, he's available on Saturday against Hull and gives the manager a nice little problem.
"You have to forget what happened in the past, maybe it was bad advice, but he's a genuine lad who just wants to play.
"He wanted to go and play somewhere but he got a game here and scored the winner which is great."
The Hammers were 2-0 up after seven minutes through Ravel Morrison - who scored after just 20 seconds - and Matt Jarvis.
But Cardiff staged an unlikely comeback thanks to a fine curler from Craig Noone just before half-time, and a first Cardiff strike for recent signing Peter Odemwingie.
However, with two minutes left Vaz Te rose highest to nod in a cross from Jack Collison and send the hosts through.
For Odemwingie, it was a first goal since his infamous January deadline-day drive to London in a bid to force a move from West Brom to QPR.
"I thought he was excellent," said City manager Malky Mackay.
"He always looked a danger and a threat but we have to get match minutes into him, he hasn't played a lot of football over the last six months.
"He's trained well but match practice is few and far between so that's something he needs to get him up to speed.
"But he's a terrific player and I'm delighted that we managed to sign him."