Celtic and Rangers are both reported to be closing in on transfers ahead of Monday night's deadline.
Reports in Italy claim Uruguay international Laxalt is on the verge of a loan move from Milan, who are one of Celtic's Europa League group stage opponents.
Celtic boss Neil Lennon said on Sunday they were "working on one or two things".
Rangers have been linked with Zungu all summer and reports in his native South Africa claim they are close to agreeing a fee with his French club.
Ibrox chiefs are not expecting any major departures, meaning Lille target Alfredo Morelos will be staying put in Glasgow unless an 11th-hour bid materialises from France.
Speaking on Friday, Gerrard – who has allowed youngster Kai Kennedy to join Inverness on loan until January – said: "There certainly won't be (multiple) additions. I think if we do well in the next couple of days there might be an addition."
Aberdeen look set to re-sign full-back Greg Leigh following his exit from NAC Breda, while Hibernian boss Jack Ross is still waiting to sign off on a six-figure deal for his former St Mirren midfielder Kyle Magennis.
Kilmarnock have bigger things to worry about after their entire squad were forced to self-isolate amid a coronavirus breakout at Rugby Park, but boss Alex Dyer has already admitted his spending is over for this year.
Livingston boss Gary Holt made his 12th signing of the current window last week with the capture of Jay Emmanuel-Thomas but may not be done yet, with the Lions still looking to strengthen further.
Dundee United have completed a move for Alaves' Cameroon international Jeando Fuchs but face an anxious wait to see if Burnley will follow up on their reported interest in striker Lawrence Shankland.
Ross County assistant boss Richie Brittain admits the Staggies are just hoping to survive the final day of the window without losing talisman Ross Stewart, who has been linked with a number of English Championship sides.
Motherwell will worry that someone may decide to test their resolve when it comes to Scotland Under-21 ace Allan Campbell, who is in the final year of his contract and is already attracting admiring looks from Aberdeen and Hibs.
St Mirren are rumoured to be on the verge of a loan deal for 19-year-old Rangers centre-half Daniel Finlayson, while St Johnstone boss Callum Davidson revealed he is close to signing Israeli striker Guy Melamed.