The winger made a big impression during his recent loan spell at The Den, scoring five goals in seven appearances, but he is now back with Saints and played in their FA Cup win over Blackpool on Saturday.
Puncheon's performances have also reportedly attracted interest from elsewhere and the fee Saints are asking is too high for Millwall.
But Jackett said: "We aren't going to match their valuation, but I wouldn't say that is the end of it and we are optimistic.
"At the moment Southampton have a very high valuation, which they are entitled to, but we can't match it."
Source: PA
Source: PA