Southampton had been linked with a move for the 28-year-old forward but Koeman's comments – in his first press conference as the club's new coach – suggest the transfer is close to being finalised.
"The situation about Pelle… it will be near to have another one in the team," Koeman said on Friday.
"It's close. But it's still not signed. But it's coming close.
"We hope maybe this weekend to have him as the second new player of Southampton."
Koeman knows all about Pelle, having coached him at former club Feyenoord, where he has been prolific since joining from Parma, initially on loan, in 2012.
Pelle – who has scored 55 goals in 66 appearances in all competitions for Feyenoord – would be Southampton's second significant signing of the close-season, following the arrival of Dusan Tadic from Twente.
