Having won the Premier League in his first season in charge, it would appear Arne Slot is keen to get his main business wrapped up early as Liverpool get ready to defend their title.
After signing Frimpong, the Reds have agreed a £116m deal to bring his Leverkusen team-mate and attacking midfielder Florian Wirtz, 22, to Anfield.
The statement signing will be a club record fee for Liverpool and he is likely to be joined at Anfield by Bournemouth left-back Milos Kerkez in the coming days.
Fresh from appointing Brentford boss Thomas Tuchel, Tottenham are interested in signing Bees striker Bryan Mbeumo. Earlier in June, Mbeumo was the subject of a bid from Manchester United of £45m and £10m in add-ons.
United and Arsenal have both been linked with Sporting's Sweden forward Viktor Gyokeres, who has enjoyed a remarkable couple of seasons in Portugal.
The former Coventry City player, who left Brighton without playing a Premier League game, has scored 97 goals in 102 appearances for Sporting.
Arsenal, who have also agreed a £51m deal for Real Sociedad midfielder Martin Zubimendi, have been linked with RB Leipzig's Slovenia forward Benjamin Sesko.
"Gyokeres has played in England before, but not for a team that's trying to win a Premier League title," former Manchester City defender Nedum Onuoha told BBC Sport.
"So, I'm not 100% sold on thinking he would be a guarantee or that he is closer to being a finished article than Sesko right now. If the manager has a liking for Sesko, I'd back him 100% and give him what he wants if the club can afford it."
There has also been lots of talk about Alexander Isak's future, but does the Sweden goalscorer really want to leave the Magpies now after helping them secure a place in next season's Champions League? It appears unlikely.
Will Crystal Palace keep their best players after winning the FA Cup?
BBC Sport's senior football correspondent Sami Mokbel said Tottenham are interested in Marc Guehi, although the Palace captain and England defender has options elsewhere.
Eberechi Eze is another who has attracted plenty of interest.
The England forward has a £68m release clause and reports have linked him with a move to Bayern Munich,, external who signed Michael Olise from Palace last summer for about £50m.