Atlanta United midfielder Almiron has arrived in Newcastle ahead of a move to St James’ Park.
The Paraguay international is set to cost a club-record fee of around £21million.
Downie claims Almiron’s signing is not likely to be confirmed until transfer deadline day on Thursday.
But he says they also want Monaco left-back Antonio Barreca and Benfica midfielder Andreas Samaris.
Downie also revealed there is a possibility of Newcastle making it four signings before Thursday’s 11pm deadline.
“I can tell you Antonio Barreca, the Monaco left-back, is currently en route to Newcastle as well,” Downie said on Sky Sports News.
“That’s ahead of a loan move until the end of the season. Benitez has been very keen on bringing in another left-back.
“On top of that, Andreas Samaris, the Greek international midfielder, there’s talks between Benfica and Newcastle over his transfer.
“That as I understand it also a loan move until the end of the season.
“And Newcastle could yet add one more but that really depends on departures from the club.
“I can tell you there has been an approach from West Bromwich Albion to take their winger Jacob Murphy on loan until the end of the season.
“And Isaac Hayden, the central midfielder who did terrifically well here last night against Manchester City, could yet be on his way.
“There has been an approach from Aston Villa for his services until the end of the season.
“A busy time I’m expecting here on Tyneside between now and the closure of the window tomorrow night.”
Barreca has made just nine appearances for Monaco since joining from Torino last summer.
Samaris, 29, has played just four times for Benfica this term.