Saints are facing a potential injury crisis ahead of the visit of Premier League champions Manchester City.
“We have several players recovering from situations that have happened to them over the last couple of games,” said Pochettino.
“I can’t confirm at the present time whether they will be ready for Saturday or not.
“I hope they will be available.
- POLL: Do you think Jack Cork will accept his new contract offer from Saints?
- RUMOUR: Saints defender linked with £20m move to United
- COMMENT: Why Saints fans are wrong if they say 'at least we can now concentrate on the league'
- Ward-Prowse rues missed opportunity for Saints
- Koeman slams Saints "very poor" defending in Palace defeat
- Saints dealt Long injury blow in Palace defeat
- Saints crash out of FA Cup on day of shocks
- Saints 2 Crystal Palace 3
“Luke Shaw has come back with a problem after his time with the England under-21s team.
“We don’t know if Adam Lallana will be ready right from the start. He is recovering from injury so we don't know yet.”
Clyne was withdrawn during last Saturday’s 2-2 draw at Wigan and subsequently pulled out of the England under-21 squad.
Ramirez suffered a similar fate with a dead leg sustained at the DW Stadium and missed Uruguay’s midweek international.
Shaw met up with the England under-21s but travelled back to Saints after picking up a knock in training with Stuart Pearce’s men on Monday.
If Shaw doesn’t make it then Danny Fox is the obvious choice to be drafted in at left back.
The Scotland international was picked by Pochettino ahead of Shaw for the game against Manchester United at Old Trafford last week.
Lallana would be the obvious replacement for Ramirez if Pochettino felt the captain was ready to start.
If neither Lallana or Ramirez are included from the start, Saints could always go 4-4-2.
For Pochettino the frustration of having players away with their international teams, and the risk of injuries that brings, is just part of the game.
“For me, they are all worthy of playing for their national teams,” said Pochettino, who won 20 caps for Argentina during his playing days.
“[But] it would be better for Southampton that they are not with their national teams after what happened to Luke Shaw.
“It's natural they should have enthusiasm to play for the national team, but they have to be calm and everything comes bit by bit over time.”