The two wireless companies agreed to a deal last year, but they are still awaiting federal approval of the $26.5 billion transaction.
"If it is really important to the administration to be first in 5G and have a more robust set of infrastructure in the U.S. than China, Japan and Korea do, then they should let the deal go through," Chaplin said on "The Exchange."
That's because Sprint is sitting on a "phenomenal band of spectrum" that can run the technology, he said. Spectrum is the airwaves networks use to provide the internet to devices. The 5G technology will enable faster data speeds.
"What Sprint has is mid-band spectrum, which can work almost everywhere. It might not be great in the most rural parts of Montana but pretty much everywhere else it's going to work great," said Chaplin, who leads the U.S. communications services research team at New Street Research.
Verizon and AT&T, on the other hand, have high-frequency spectrums, which work great in the big cities but not very well outside of dense markets, he noted.
The problem is, Sprint doesn't have the money to deploy its spectrum band, he added.
"If the deal with T-Mobile goes through, that's going to put those companies in a phenomenal position. If the deal doesn't go through, that spectrum just sits on the sidelines for the next five years."
Trump held an event on 5G at the White House on Friday with Federal Communications Commission Chairman Ajit Pai, announcing a $20 billion fund to build out high-speed broadband networks in rural America. The FCC also intends to start the agency's third 5G spectrum auction on Dec. 10.
"The race to 5G is on and America must win," Trump said, noting that 92 5G markets will be ready by the end of the year, outpacing South Korea, which is on pace to have 48 markets live by the end of 2019.
"To accelerate and incentivize these investments, my administration is freeing up as much wireless spectrum as needed," Trump said. "[We're] removing regularity barriers to the buildout of networks.The FCC is taking very bold action, bolder than they've ever taken before, to make wireless spectrum available."
It's an issue the president has been pushing for. In February he called on U.S. companies to step up their efforts on the technology.
The White House had no comment on Chaplin's remarks.
— CNBC's Todd Haselton and Reuters contributed to this report.