Saints are understood to have reluctantly felt they had little choice but to allow Rickie Lambert to speak to Liverpool about a move to Anfield.
The club received a surprise approach from the Reds yesterday, and have now agreed a fee worth as much as £5m up front, plus add-ons.
Liverpool are understood to have insisted the deal took place before the end of the weekend, otherwise they would have to turn their attention elsewhere, saying they would be unwilling to wait until after the World Cup.
While Saints would like to have kept Lambert, they were aware that the move represents a dream one for him and that standing in his way could create a deep and unhealthy division with the player.
Although chairman Ralph Krueger had said before Liverpool's bid arrived that all transfer dealings were on hold until a replacement for Mauricio Pochettino was appointed, had Saints kept him against his wishes there were fears that the club would have to accept a lesser fee for him later this summer if it meant the relationship moving beyond repair.
Lambert, who could feature for England in tonight’s World Cup warm-up against Peru at Wembley, is set for a medical tomorrow, and will sign a two-year deal if he passes that.