The 26-year-old will captain the Hammers in their Europa League qualifying clash with FC Lusitans on Thursday night with a number of other first-team regulars not involved.
Bilic replaced Sam Allardyce on June 9 but will not take charge of the match, with academy boss Terry Westley in the dug-out.
The former Croatia manager will be in attendance at a sold-out Upton Park and Tomkins admits he was a big fan of Bilic when he turned out for the Hammers between 1996 and 1997.
“Yes, certainly he is someone who certainly showed his passion on the pitch,” Tomkins said when asked if he remembered Bilic’s 18-month spell at West Ham fondly.
“I remember him as a player he didn’t play as many games as you’d think for someone who has the likeability he has got around this place but it is because of that passion he showed during those games and I’m sure he does that in managing as well.
“The fans love that, he wears his heart on his sleeve and put his all into tackles, people want to see that.”
Tomkins is one of three senior central defenders along with Winston Reid and James Collins, but Bilic has been linked with a number of re-enforcements in the summer transfer window.
Former England Under-21 international Tomkins, who missed the end of last season with a dislocated shoulder, wants to use Bilic’s experience as a well-respected defender to better his own game.
When asked if he was looking forward to learning from Bilic, Tomkins said: “Definitely. I had a little meeting with him and I said ‘I’m looking forward to working with you’.
“If he can improve my game it will only benefit me as a player and I’m sure he will take our defending sessions and it will be nice to see what ideas he has got and if he can improve us as players.
“That is what I want, I want to keep improving, I’m 26 years old and I think defenders develop later on in their careers and I want to progress my game further and if I can do that with the new manager that would be brilliant.
“He was an international and has managed at international level, you don’t get much bigger than that – he is very intelligent and knows his players.
“All good managers have that presence. As soon as they come into the room you can hear a pin drop at times. that is the kind of presence he has got.”
Tomkins has been working closely with Westley and fellow first-team regulars Matt Jarvis, Morgan Amalfitano, Diafra Sakho and Joey O’Brien in preparing for the game against Andorran minnows Lusitans.
The remainder of the squad are in Ireland with Bilic, who will fly back for Thursday’s game, and Tomkins is looking forward to playing in front of a full house as West Ham get back onto the European stage for the first time in nine years.
“I’m massively excited, playing in Europe is massive,” he said.
“We all want to play on the top stages, playing against teams from different countries, different cultures, it can only improve you as a player, develop you, so we are all really excited, for the youngsters it’s an opportunity.
“There are 35,000 people. Not many other teams would sell that many tickets for an Europa League game.”