Southampton have agreed a fee with Basel for Norwegian international Mohamed Elyounoussi, Sky Sports News understands.
The fee is understood to be in the region of £16m.
The 23-year-old, who has 16 caps for Norway, can operate as a forward or as a winger.
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Elyounoussi scored 14 goals in 45 appearances last season, including two in the Champions League as Basel advanced to the last 16 before being knocked out by Manchester City.
The signing of Elyounoussi would boost Southampton's forward options, with Serbian international Dusan Tadic looking set to leave the club.
Dutch giants Ajax are close to agreeing an £18m deal for Tadic, who has told the Saints he wants to return to the Eredivisie, where he previously played for FC Twente and Groningen.
Sports News understands negotiations between Ajax and Southampton are at an advanced stage and a deal is likely.
No Southampton player had more goals or assists than Tadic last season and he scored twice in the win against Bournemouth which inspired their last minute climb out of the relegation zone.