The England World Cup squad goalkeeper was the subject of an offer described as "derisory" by Celtic, who would not consider letting the 26-year-old go unless an offer close to £9m is received. Southampton are believed to have bid less than half of that sum.
Forster kept a clean sheet last night as Celtic dismissed KR Reykjavik 4-0 in their Champions League second qualifying round, second leg at Murrayfield, going through 5-0 on aggregate. Celtic will face either St Patrick's Athletic or Legia Warsaw in the third round next week although it remains to be seen if Forster will still be with them by then. Deila's message was emphatic, though: Celtic were determined to keep all their senior players.
"We want to keep Fraser," he said. "We want to qualify for the Champions League and build our team further. So we want to keep him here. He has not indicated any desire to leave. He came to Celtic and has done a good job here, but Celtic has also been fantastic for him. I hope that continues because we need our best players and he is a fantastic goalkeeper.
"In the end, something will happen, but whether it happens now or in the winter or next summer I don't know; we just have to keep on going. Things happen around my players all the time. But Fraser is an unbelievable professional and I know he wants to play in the Champions League."
When asked about the precise size of the Southampton bid, Deila said: "You have to ask Peter [Lawwell, the chief executive]."
St Pat's face Legia Warsaw tonight with the tie poised at 1-1 after the first leg in Poland. Celtic will be favourites to beat either of them after an easy rout of the Icelandic champions. Virgil van Dijk scored twice and Teemu Pukki once in the first half hour, before Pukki added a late second for 4-0.
"I was happy with their attitude," said Deila. "They started very well, the first 30 minutes killed the game. In the second half we wanted to go out and do the same things. I didn't think we managed that. That's something we have to work on in the future; to have 90 minutes and really destroy an opponent. When we have three goals we want to go for more. It's important to have every minute on the pitch to progress. We want to be direct with the ball and we want a lot of movement. It's early in the season but we are taking steps in every match."
Deila smiled when it was put to him that there had been some mild booing when Pukki was substituted after his second goal. "I will have that in my mind the next time, if they start booing! Pukki was good. He had a lot of chances. He just has to continue. He has scored in almost every game he has played now."
The tie was at Murrayfield because Celtic Park was out of commission to Celtic because of tonight's Commonwealth Games opening ceremony.
"I was very happy with Murrayfield," said Deila. "The fans were unbelievably good, there were a lot of people here, the pitch was fantastic and there was a good atmosphere in the stadium. I think the next round will be even better."