Celtic have offered a trial to Brazil right-back Coelho and the 24-year-old is expected to arrive in early January.
Coelho is still under contract with Corinthians
Coelho is nearing the end of a year-long loan from Corinthians to Brazil rivals Atletico Mineiro.
And Celtic boss Gordon Strachan said: "I think he is coming over in early January to have a look at the place.
"I do feel that the squad needs some help, especially at the back. We are trying bring in players that are definitely going to make us better."
Strachan turned to the Brazilian after Andreas Hinkel decided against a move from Sevilla to Celtic Park and instead chose Borussia Dortmund.
Long-term injuries to Mark Wilson and Jean-Joel Perrier-Doumbe have led to central defender Gary Caldwell filling in at right-back.
When you are playing with four centre backs and you have a young winger playing at left-back, you know that all is not comfortable back there
Celtic manager Gordon Strachan
On the other flank, Lee Naylor's absence has seen midfielder Paul Hartley, centre-back Darren O'Dea and young Ryan Conroy being used as emergency cover.
"When you are playing with four centre backs and you have a young winger playing at left-back, you know that all is not comfortable back there," said Strachan.
"Young Ryan has come in and done very well for us, but he was a winger.
"We had to give him a crash course in being a left-back.
"You look at the best defensive teams and they play the same back four all the time, but we've not had that opportunity so we will try and rectify that."
Corinthians president Andres Sanchez had been quoted as saying that his club had received an offer from Celtic that was "favourable for the club and the player".
Coelho, who is under contract until July 2009, won his only cap for Brazil in 2003, when he was substitute in a defeat by Mexico in the Gold Cup final.
He also helped Brazil win the Under-20 World Cup that season.
Coelho was controversially banned for 120 days in September after elbowing Cruzeiro's Kerlon.
The teenager was challenged during one of his trademark "seal dribbles" where he flicks the ball up and bounces it on his forehead as he beats opponents.
Coelho's ban was reduced to five games following an appeal by Atletico.