According to speculation from the Spanish media cited by Portuguese sports tabloid Record, prospective new Valencia owner Peter Lim rejected proposals worth approximately €18 million from both Premier League clubs, with Gomes having only joined the La Liga outfit from Benfica this summer.
The same source further claims that teammate Rodrigo also received transfer interest as both players are currently only on loan at the Mestalla until Lim's takeover is fully complete and ratified.
21-year-old Gomes has made two appearances so far in his first season at Valencia and featured on 14 occasions during Benfica's eventful 2013/14 campaign that saw them win the Primeira Liga and the Portuguese Cup as well as make - and lose - the final of the Europa League for the second year in succession.
A versatile midfielder, he has yet to make his Portugal debut at senior level at but has gained extensive experience at every youth stage from the U17s right up to the U21s.
While Manchester United and Manchester City will have been disappointed to miss out on Gomes, the two bitter North-West rivals still appeared to enjoy successful windows.
In contrast to the way things have developed over recent years, it was actually the former who made the biggest impact in the summer market, with Angel di Maria and Radamel Falcao the most notable additions to Louis van Gaal's squad at Old Trafford.
City, meanwhile, were mostly sensible with regards to their own transfer business, with Manuel Pellegrini evidently eager not to upset the balance of the side that secured their second Premier League title in three seasons last time out.
Argentine goalkeeper Willy Caballero - a player Pellegrini knew well from his spell in charge of Malaga - was brought in to provide cover for Joe Hart following the departure of Costel Pantilimon, promising French defender Eliaquim Mangala arrived in a big-money move from FC Porto while Bacary Sagna joined on a free, Frank Lampard arrived on a loan deal and Bruno Zuculini was purchased from Racing Club for a nominal fee.