Reports coming out of the Devon club suggest that the Millers have agreed a £500,000 fee for the 26-year-old.
Ladapo scored 18 goals in an Argyle team that was relegated from League One last season and Millers boss Paul Warne wants to bring him to South Yorkshire.
Sunderland are also thought to be keen on landing the former Crystal Palace man, but Portsmouth are no longer in the race.
Signing Ladapo would be a real statement of intent by the Millers as they look to build a squad capable of bouncing back to the Championship at the first attempt following relegation last term.
It will be the most they have ever spent on the player, having previously spent around £400,000 on Jon Taylor three years ago.
The most they have ever spent on a striker is £250,000 for Jordan Bowery in 2014.
If the move comes off, and there is nothing official coming from the club, he would join a strikeforce that already consists of Michael Smith, Jamie Proctor and Carlton Morris.
It was a breakthrough year for the 26-year-old last season as he enjoyed his best ever goalscoring return.
He joined Argyle following his release from Southend and it was his 11th club.
With the Millers soon set to bring in excess of £3million from the sale of Will Vaulks to Cardiff, they will have some money to play with.
But chairman Tony Stewart is insistent that they will never throw cash around.
“We'll never burst the bank," he said.
"At the end of the day, we owe it to Rotherham United and we owe it to the town to make sure we have got a sustainable vision for the future.
"We'll always stay in Rotherham. We have a nice stadium, good people working for the club and fans who have celebrated the good football we have played. I want to retain that.”
"Our main priority is to get back into the Championship next season, or the season after, and prove we are capable of maintaining a place there, whether it's fifth from bottom or 10th from bottom.
"Obviously, like with any businessman, if you're putting the investment in, you want a return."