Investors are becoming too relaxed about the future direction of the Federal Reserve and need to pay closer attention to the composition of its next board of governors, a strategist told CNBC.

The next leader of the U.S. Federal Reserve will be named Thursday and most expect President Donald Trump to have chosen Jay Powell, a member of the Fed’s current board. What’s not so certain is who will be the next Fed chief’s closest advisers and what influence they could have on the bank and, ultimately, markets.

“The tricky part of this story is that we get Powell (as Fed chair, if he’s nominated) but what happens to the other three seats (on the Fed’s board of governors)?” Luis Costa, head of CEEMEA FX and rates strategy at Citi, told CNBC Thursday.

“We are not getting the definition of the other three seats,” he said. “We’ve got the vice governor and the other two seats and they can actually stay empty for a while and we are talking about a big chunk of the decision-making power in the board,” he said.

It’s expected that Powell will be announced as the next chair of the Fed and would succeed Janet Yellen when her term ends in February. A lawyer and former undersecretary of the Treasury, Powell is considered a solid and even “boring” choice. While not an economist, he is experienced at the Fed, having been appointed a governor in 2012. With this background, Powell is expected to steer a similar course to Yellen of gradual rate hikes but also could bring about some deregulation of financial markets.

As such, he is a popular choice for traders with stock markets seemingly sanguine at the prospect of a Powell-run Fed.

However, Costa believes that financial markets are too complacent over the future direction the Fed could take, saying that it was not unfeasible for a more hawkish member of the Fed — such as economist John Taylor who advocates higher interest rates — to become the vice-chair and advocate a more hawkish monetary policy and faster rate hikes.

“The markets are — for want of a better word — (demonstrating what I call) ‘dumb flows’,” he said. “OK with Powell … apparently nothing has changed at the board, which is the wrong reading (for markets to have).”

Costa forsaw the possibility for a more-balanced board of governors at the Fed but “not necessarily biased towards the dovish side.”

“Depending on its composition, I think the board could be departing from this view and already we’re seeing central banks trying to depart from this view. Inflation is not going anywhere and our monetary policy (of low rates) is not going anywhere, things are changing — probably not at the pace that hawks are expecting but things are changing,” he added.

Andrea Ianelli, investment director at Fidelity International, told CNBC Thursday that the idea of the Fed being on “auto-pilot” and carrying on as before should be a “red flag” to markets and that “one should also try and expect the unexpected sometimes.”

“The fact that Powell is seen as the more likely candidate to follow in Yellen’s footsteps gives a sense of continuity to the market, to the Fed,” he said. “The December meeting seems to be something of a done deal and a lot of focus will be on the upcoming unemployment report and on wages but so far it’s all priced in. So in terms of room for meaningful surprises there’s not a lot there,” Ianelli said.

“However, what can go wrong is and what can spook the market is if we see some derailment in the tax negotiations that are still ongoing in Washington. As we know, these negotiations can take longer than the market expects and the final shape of the bill might be different from what we’ve seen so far.”

– CNBC’s Patti Domm contributed reporting to this story.