Manchester United have been told they will have to pay between £70m – £90m to sign the Argentine star.
But Solskjaer will only look to move for Dybala if one of Romelu Lukaku or Paul Pogba departs Old Trafford, according to the Daily Mail.
Both United stars have made their feelings clear as they seek new challenges away from Manchester.
Pogba has been linked with a return to Juventus, potentially leaving a hole in the United attack which Dybala could fill.
Solskjaer is an admirer of Dybala and recognises the need to strengthen in the majority of areas in his squad.
The Norwegian believes the 25-year-old can add a spark to the Red Devils attack.
Cristiano Ronaldo’s arrival in Turin has had an affect on many of the Juventus squad – predominantly the forwards.
Dybala had the least fruitful season of his four years at the Allianz Stadium scoring just ten times.
Rumours earlier this summer, via Dybala’s agent and brother, suggests he didn’t want to play second fiddle to Ronaldo and was ready to move on.
He has since dismissed those claims, but Juventus are prepared to listen to offers to him.
United do face competition from PSG and Inter Milan for Dybala’s signature, but it is understood Dybala would not entertain a switch to the San Siro.
New boss Maurizio Sarri is relaxed on the situation regarding the Argentine.
He has contemplated several options, one of which is turning Dybala into a centre forward thus allowing him more opportunities in front of goal.
But equally he would not be opposed to seeing him leave the Serie A champions provided he was able to reinvest the money this summer.
The Bianconeri have already spent in excess of £100m on the likes of Matthijs de Ligt and Luca Pellegrini while also adding Aaron Ramsey and Adrian Rabiot on free transfers.