The France international remains a part of the Reds’ Under-23 squad since his falling out with Jurgen Klopp.
Liverpool’s manager is still hoping to offload the 26-year-old on a permanent basis this month, with Tuesday’s deadline fast approaching.
There is interest in signing Sakho from Premier League sides, according to the Liverpool Echo, although Liverpool’s asking price and the defender’s wages make him expensive for relegation-threatened clubs.
The Reds may apparently let Sakho leave on loan if all other options are exhausted though.
Mamadou Sakhohas not played for Liverpool's first team since last April
My answer to this might remind certain people about a song. When there is PSG, Sakho is with them
And there are also links back in his homeland of France, but the former Paris Saint-Germain centre-half will not contemplate joining their Ligue 1 rivals Marseille.
“Since I started this incredible adventure abroad, in terms of football but also in terms of my family, because when I see my children speaking English I think it is a glorious thing that I have been able to give them,” Sakho told Canal Football Club.
“I think I have a few more wonderful years to experience abroad first. And PSG, why not, but afterwards.
“I think Marseille have a very good team. Bafé (Gomis) and Pat (Evra) are friends of mine. But my answer to this might remind certain people about a song. When there is PSG, Sakho is with them.”
Mamadou Sakho scores for Liverpool U23s in pictures
Sun, November 20, 2016
Click through the gallery for the best snaps of Mamadou Sakho scoring for Liverpool U23s
Liverpool FC via Getty Images
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Click through the gallery for the best snaps of Mamadou Sakho in action
On his current situation at Liverpool, Sakho added: “I work a lot, I have the chance to train with the reserve team, which allows me to keep up.
“And beside that I have my trainer. So I work a lot to stay on top of my game."
With Virgil van Dijk ruled out for three months at Southampton and Jose Fonte sold to West Ham, Claude Puel is looking to add defensive cover.
Meanwhile, Palace and Swansea have struggled defensively this season and would benefit from Sakho’s experience should either broker a deal.