Alexander Isak returned to training at Newcastle United on Monday after missing the club's preseason tour of Asia amid ongoing speculation over his future.
Isak had been training at his former club Real Sociedad to rehab a "minor thigh injury" that the club said meant he did not take part in the friendly matches in Asia.
ESPN reported last week that Liverpool had a bid worth up to £110 million (($197 million) rejected for Isak and that the club were not planning a follow-up offer unless Newcastle sign a replacement striker.
The bid was well below Newcastle's £150m ($197m) valuation of Isak, a source told ESPN the nature of Newcastle's rejection was such that Liverpool feel presenting a second bid at this juncture would be pointless.
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Newcastle boss Eddie Howe had described the situation as "far than ideal."
Newcastle have been in the hunt for a striker themselves that saw them make a bid worth worth €80m ($106m) for RB Leipzig striker Benjamin Sesko, although it was reportedly rejected.
Manchester United also hold a strong interest in Sesko. Contact has been made between the two clubs and talks are ongoing.
