Saints have seen several of their key players leave the club this summer following relegation from the Premier League.
Martin is expecting Southampton to be active in the last couple of weeks of the window as he seeks to strengthen the squad in the coming days.
The Saints boss has identified Leeds right-back, Drameh, as a long-term target for the south coast club.
Martin is pushing Southampton to try and snare the 21-year-old away from Leeds in the ongoing transfer window.
The Southampton manager is a big fan of Drameh and is prepared to draft him into the team as soon as possible if he can sign him this summer.
However, Martin is prepared to play the long game and is ready to wait until January or next summer for the defender.
Drameh has entered the final year of his contract at Leeds and will be available for a compensation fee at the end of this season if he does not sign a new deal.
He has not featured for Leeds in the Championship thus far but played in an EFL Cup game last week.
