It depends a bit on how you have these logs on those linux servers. If that is all syslog based, you should be able to configure the syslog daemon on these linux servers to forward data to your intermediate forwarders (by setting up a TCP/UDP network input on those).
But that is typically not recommended. The recommended approach is to wherever possible install a UF on the source, as that significantly improves reliability, configurability etc. of the data collection.