U.S. President Donald Trump will likely welcome the Federal Reserve's projection of zero interest rate hikes this year — but he should be wary that his hopes for a strong American economy may not materialize, according to a former Fed governor.

Trump has on several occasions last year hit out at the U.S. central bank for raising interest rates, claiming that such an action was harmful to the American economy. But if the economy were to be as strong as Trump wanted, the central bank would have to hike interest rates, said Robert Heller, a member of the Fed's Board of Governors from 1986 until 1989.

"President Trump hasn't been saying much recently about the Federal Reserve and he should be very happy with the current stance — but he also has a dilemma, a conundrum if you want to call it," Heller told CNBC's "Capital Connection" on Thursday.

"On the one hand, the administration says the economy will grow, perform really well ... On the other hand, they want to have low interest rates. You really can't have it both ways," he added.

Economic expansions are frequently a trigger for inflation — but if the sustained increase in prices goes out of hand, it could erode buying power and hit confidence in a way that hurt growth.

To prevent inflation from reaching levels that could harm the economy, central banks usually raise interest rates so that companies and individuals find it more costly to borrow money. That will in turn help tame over-exuberance in economic activity and inflation.