Kristoffer Ajer has completed a medical with Brentford ahead of a £13.5m transfer from Celtic.
A deal for the 23-year-old Norway centre-back has largely been agreed with only the final details to be concluded.
Ajer, who is highly rated and also a target for fellow Premier League newcomers Norwich, was not in Celtic's squad for their first pre-season friendly at the weekend.
Celtic are preparing to play Brentford's sister club FC Midtjylland in a Champions League qualifier on Tuesday night and Ajer is not expected to be involved.
Brentford have already completed the signing of FC Midtjylland's Frank Onyeka after he received a work permit.
The Nigeria midfielder has been announced as the Bees' first signing as a Premier League club on a five-year deal after arriving in the UK on Sunday.
Onyeka is quarantining in line with Covid-19 travel restrictions before joining up with his new team-mates for pre-season preparations.
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Sky Sports News revealed earlier this month the 23-year-old had agreed to sign for Brentford.
He remained in Denmark during the work-permit process, where he completed a medical and continued to train with his now former club.
A deal between the clubs was a formality to conclude because they are both owned by Matthew Benham.
Brentford have made strengthening at right-back, right centre-back, midfield and on the wings their priority this summer as they prepare for their first season in the top flight.
Right-back Henrik Dalsgaard has moved in the opposite direction to Midtjylland, and attacker Emiliano Marcondes has left the club, while top-goalscorer Ivan Toney is being tracked by other clubs.
Frank: Fans can expect something soon
Brentford boss Thomas Frank suggested to Sky Sports News that the deal for Ajer could be completed on Wednesday.
Speaking after his side's pre-season friendly victory over Boreham Wood on Tuesday night, Frank said: "There's rumours about a new player, let's see what's happening tomorrow.
"Let me put this way, I think they (the fans) can expect to see something soon, yes."
Frank also said that there is scope for further arrivals at the newly-promoted club, despite him being "pleased" with his current group of players.
"We will be on top of everything happening in the market," Frank added.
"I think we have a very strong squad - I'm pleased with that but of course if we can get the right players in at the right price that fit the right profile, then maybe there'll be more (signings)."