The Welshman was sacked on Monday (20 November) and Albion's Chinese owner, Guochuan Lai, was reportedly interested in speaking to the Croatian, whom he had identified as one of the potential replacements for Pulis.
However, according to the Daily Mail, the 49-year-old has turned down the Baggies' approach as he feels returning to the Premier League only a few weeks after being sacked by West Ham might be too soon.
Bilic's two-and-a-half-year spell as Hammers boss came to an end after a 4-1 defeat to Liverpool on 4 November and the former West Ham and Everton defender has been spending time with his family since.
Bilic, who led West Ham to a seventh and 11th place finishes during his spell in east London, is understood to have told the Baggies that he would prefer to extend his break until 2018, before evaluating his options.
The former Croatia manager's snub further complicates West Brom's plans to find a replacement for Pulis, after Sam Allardyce appeared to rule himself out of the running on Thursday (23 November).
The former England manager, who has not managed in the Premier League since guiding Crystal Palace to safety last season, had emerged as one of the candidates to take over at The Hawthorns.
However, according to the Mirror, the 63-year-old is eager to manage an international side again and is unlikely to hold negotiations with West Brom, who are currently fourth from bottom in the league.
With Bilic and Allardyce seemingly uninterested, the door remains open for other candidates, including Nigel Pearson and Alan Pardew.
The former, who is currently employed by Belgian Second Division side OH Leuven, knows the club well after serving as assistant to Bryan Robson at The Hawthorns between 2004 and 2006, while the latter is still looking for a job after being sacked by Palace in December last year.
The 56-year-old would certainly be welcome by West Brom's technical director, Nicky Hammond, who was given his first coaching role by Pardew, when the latter was in charge of Reading.
Meanwhile, Pulis' assistant Gary Megson, who managed West Brom between 2000 and 2004, has been appointed as caretaker and will take charge of the Baggies' trip to Wembley Stadium to face Tottenham Hotspur on Saturday [25 November].
A dismal run of results has left West Brom just one point above the relegation zone after four consecutive defeats in the Premier League, a competition in which they are without a win since the end of August.