Jurgen Klopp's Liverpool side have not been able to call upon Naby Keita as much as they would have liked this term.
Keita and Oxlade-Chamberlain have both had their progress at Liverpool thwarted by injury problems in recent times.
But Carragher wants the Liverpool duo to be given more time to prove themselves at Anfield, as he thinks they could come on strong next term.
And he has suggested that Klopp's first priority in the summer should be to buy a striker, rather than a midfielder.
“I think in defence they have four centre-backs, they have young players coming through in full-back positions. In midfield we are still waiting for Naby Keita and Oxlade-Chamberlain to explode, so give them more time,” Carragher said.
“The biggest thing Liverpool need to spend on is an attacking player.”
Keita has made just eight Premier League appearances this term, after another season blighted by injury problems.
When he does make it on to the pitch, Keita is arguably Liverpool’s most creative option.
However, if he struggles for fitness again next season, it could be that Jurgen Klopp’s patience with him runs out.
Oxlade-Chamberlain, meanwhile, has been fit more regularly for Liverpool, but is yet to really nail down a starting place.
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