Kovacic would be an exciting signing but we should aim for a DM who protects our defence and provides a good connection to the midfield. Of course, someone like Schneiderlin or Witsel would be perfect for that role but that's never going to happen. I would've loved Nainggolan as well although he's more of a box-to-box guy but it seems that's impossible as well. I don't have a clue as to who it's going to be, but we definitely need one.
As for the striker, there are still a lot of good players out there who're attainable. Bacca (despite his age), Benteke (despite the quoted price), Martial (more of a gamble but worth a punt), Lacazette, Jackson Martinez and Higuain (not gonna happen), and probably plenty of others. We do need one though, Sturridge isn't even fit for the start of the season and we can't have Ings as our primary option if we want to be genuine competitors for top four. Firmino can do a job up front as well but I'd rather see him behind the striker alongside Coutinho.
I too think a DM would be the order of the day. The two players you mention are out of the question but Illara would be a good buy, imo. He is a good holding player with good passing range. He would suit you well.
Striker is the tricky one. Bacca already confirmed that he is going to Milan, Martinez is joining A.Madrid and don't see much chance of Liverpool signing Lacazette, or Higuain. Benteke is the best bet but I wonder if he is the man Rodgers needs for the style of football he wants to play.
All in all a good summer window for 'Pool. Whether it is good enough to usurp any of the top 4, is anybody's guess at this moment.