Manchester United had an opening bid worth in excess of £40m for Aaron Wan-Bissaka rejected by Crystal Palace this month and are weighing up whether or not to make an improved offer for the England Under-21 international.

Wan-Bissaka enjoyed an eye-catching first full season in senior football in 2018-19 after graduating through the south London club’s academy, excelling at right-back and making 39 appearances in all competitions. The 21-year-old, originally a winger, is currently preparing for the summer’s European Under-21 Championships in Italy and San Marino, with United having earmarked him as part of a radical revamp of their backline.

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The sizeable opening offer was apparently tabled by United at the beginning of the month and rejected immediately by Palace. Wan-Bissaka is contracted at Selhurst Park through to 2022 with neither player nor club in any great rush to move on. It remains to be seen whether an offer closer to £60m might yet be considered more seriously.

“I am with Crystal Palace at the moment,” said the full-back earlier this month. “That is where my contract is and that is where I will be next season. I have got three [years] left on my contract. It says I am going to be there, so that is all I can focus on now.”

United are seeking to bolster Ole Gunnar Solskjær’s options after a hugely disappointing end to the season in which they tailed off after a promising start under the Norwegian’s management and eventually missed out on qualification to the Champions League.

They have released Antonio Valencia among 14 players who are out of contract this summer, and are seeking to strengthen significantly across their defence after conceding 54 Premier League goals last season. They are close to securing the Wales winger, Daniel James, from Swansea City after having a fee that could rise to around £18m accepted by the Championship club.

Palace have been braced to field interest in their Ivory Coast winger Wilfried Zaha, who has made clear his desire to play in the Champions League. Yet they value Zaha, who is contracted to 2023, as high as £100m and would not countenance losing both him and Wan-Bissaka over the summer.

Meanwhile, West Ham are in talks with Celta Vigo over the signings of Maxi Gómez and Stanislav Lobotka.

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Manuel Pellegrini is determined to strengthen in central midfield this summer and has targeted Lobotka after attempts to woo Barcelona’s André Gomes ended when the Portugal international made it clear he favours a move to Everton. West Ham have indicated they are willing to pay £30m for Lobotka, a 24-year-old Slovakian international who has been compared to Real Madrid’s Luka Modric, and are optimistic a deal can be agreed.

However, West Ham are also keen to bring in a new striker after releasing Andy Carroll on a free transfer and selling Lucas Pérez to Alaves and are attempting to negotiate an ambitious double deal with Celta which would see Gómez and Lobotka both move to the London Stadium for a combined €60m (£53.5m). Pellegrini is a big admirer of Gómez, although West Ham are reluctant to trigger the Uruguayan’s release clause of £43.5m.

Facebook Twitter Pinterest Maxi Gómez celebrates scoring for Celta Vigo against Barcelona in December 2017. Photograph: Alejandro Garcia/EPA

West Ham, who are also tracking Lorient’s Alexis Claude-Marice, West Bromwich Albion’s Salomon Rondon and Fulham’s Aleksandar Mitrovic, identified Gómez as a potential replacement for Marko Arnautovic when the Austrian attempted to join Guangzhou Evergrande in China in January. Their interest in Gómez has not faded, although they could face competition from Valencia for a 22-year-old striker who has scored 30 goals in 71 league appearances for Celta.

West Ham’s director of football, Mario Husillos, has also targeted the Olympiakos attacking midfielder Kostas Fortounis, who has a year left on his contract with the Greek club. However West Ham have yet to come up with a suitable offer for the Greece international. It is thought that Olympiakos want at least €17m, although Fortounis’s preference is to extend his current deal rather than move to the Premier League.

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Pellegrini is likely to have to raise funds through sales in order to keep strengthening his squad. West Ham sold Edimilson Fernandes to Mainz for £8m last week and will listen to offers for Javier Hernández, Pedro Obiang and Angelo Ogbonna. Obiang wants to move to Italy for family reasons.

Reece Oxford’s £4m move to Augsburg remains in the balance. The 20-year-old defender spent the second half of last season on loan with the Bundesliga club, but there are issues over personal terms to resolve before the transfer is finalised. A source close to the deal rated the chances of it being completed as 50-50.