The Brazilian top player noticed the issue prior to the 3-1 Champions League win against AC Milan on September 17, and it worsened during the match.
“Alisson is still a doubt if he can train today, so let’s wait (to see) if he can train,” Slot said on Sept 20.
“If he can’t, he probably won’t play as well. He has a slight issue with one of his muscles, and we wonder if this game is coming too early or not.
“Now we have to wait and see if he’s ready to be in goal (on Saturday) or we have to wait a few extra days.”
Caoimhin Kelleher, who played the majority of pre-season for Liverpool with Alisson busy at the Copa America, would replace the Brazilian if he is not fit.
Alisson has conceded just two goals in five games in all competitions this season, with Liverpool enjoying a good start under new manager Slot.
They are fourth in the league table after four games, trailing leaders Manchester City by three points. The Reds won their first three matches without conceding a goal, before a shock 1-0 loss to Nottingham Forest the last time out.
However, they got back to winning ways by dominating Milan at San Siro in their return to the Champions League after a year’s absence from Europe’s top competition.
“It was not only about bouncing back after loss against Forest,” said Slot when asked if his team are back on track.
“The Liverpool teams of the past and some of these players have set high standards in Europe and we have to try to get back to those standards and we have made a good step.
“The performance shows we can dominate in a stadium that is not Anfield.”
Harvey Elliott is expected to be the only other absentee for the match against Bournemouth.
The Cherries, who have lost 11 of their 14 Premier League matches against Liverpool, are 11th in the table on five points after beating Everton along with two draws against Forest and Newcastle, and a defeat by Chelsea.
“Bournemouth started off quite well with a win against our neighbours,” Slot added.
“The manager has done a tremendous job there, nice football to watch and has developed players. They were aggressive here last season (Liverpool won 3-1) and scored a goal off a high press and we expect the same.”
It is still early in the season, but the Dutchman was also asked about his thoughts about managing in the Premier League so far.
He said: “Until now I haven’t seen anything different but Premier League has four extra games and the League Cup. From the start to now we’ve played just as many games as at Feyenoord – that’s not an issue to me.
“But main difference with Premier League to Europe is we have to play at Christmas and New Year. And the quality of the league, of Forest and Bournemouth, is much much higher than if you play in Eredivisie against a team not challenging for the top six.”