The World Cup-winning midfielder was caught by a high tackle from Jonjo Shelvey during a recent victory over Newcastle.
He suffered enough damage to keep him out of an FA Cup third-round clash with Reading.
Pogba was also late joining up with United for a warm weather training camp in Dubai as he continued to receive treatment.
He has, however, linked up with the rest of his team-mates in the Middle East as they prepare for a return to Premier League action on Sunday.
Solskjaer believes a man who has enjoyed a welcome return to form in the wake of Jose Mourinho’s departure could figure at Wembley Stadium, while updates have also been offered on a couple of other absent stars.
United’s interim manager told the club’s official website: “Marcos [Rojo] has gone back home because his injury is taking a bit longer than we thought.
“Fred[‘s partner] is expecting a baby and Paul [Pogba] has had his knock and has had a few days of treatment back home.
“Hopefully, we can get Paul on his feet during this week”he said
He helped Solskjaer to open his spell at the helm with a run of four successive wins in the Premier League, before Reading were then seen off in cup competition.
United will be eager to get him back into their side as soon as possible, especially as a visit to Spurs presents them with a chance to close further on the top four.
Marcos Rojo, who has made just three appearances this season, will not figure as his fitness struggles continue.
Eric Bailly will also be absent as he serves the final instalment of a three-match ban for the red card he picked up against Bournemouth, but fellow centre-half Chris Smalling has stepped up his recovery from a foot complaint.